@Preamble{"\def\noopsort#1{}" # "\def\l{\char32l}" #
"\def\v#1{{\accent20 #1}} \let\^^_=\v" #
"\def\hbk{hardback}" #
"\def\pbk{paperback}" #
"\ifx \undefined \booktitle \def \booktitle #1{{{\em #1}}} \fi" #
"\ifx \undefined \mathrm \def \mathrm #1{{\rm #1}} \fi" #
"\ifx \undefined \pkg \def \pkg #1{{{\tt #1}}} \fi"
}
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|http://www.math.utah.edu/~beebe/|"}
@String{ack-njh = "Nick Higham,
e-mail: \path|nick.higham@manchester.ac.uk|"}
@String{inst-CS-U-MARYLAND = "Department of Computer Science, University
of Maryland"}
@String{inst-CS-U-MARYLAND:adr = "College Park, MD, USA"}
@String{inst-CS-U-TENN = "Department of Computer Science, University
of Tennessee"}
@String{inst-CS-U-TENN:adr = "Knoxville, TN, USA"}
@String{inst-CS-U-UMEA = "Institute of Information Processing,
University of Ume{\aa}"}
@String{inst-CS-U-UMEA:adr = "Sweden"}
@String{inst-HARWELL = "{AERE} {Harwell} Laboratory"}
@String{inst-HARWELL:adr = "Chilton, Oxon, England"}
@String{inst-MCCM = "Manchester Centre for Computational
Mathematics"}
@String{inst-MCCM:adr = "Manchester, England"}
@String{inst-MCS-ARGONNE = "Mathematics and Computer Science Division,
Argonne National Laboratory"}
@String{inst-MCS-ARGONNE:adr = "IL, USA"}
@String{inst-MIMS = "Manchester Institute for Mathematical
Sciences, The University of Manchester"}
@String{inst-MIMS:adr = "Manchester, UK"}
@String{inst-ORNL = "Oak Ridge National Laboratory"}
@String{inst-ORNL:adr = "Oak Ridge, TN, USA"}
@String{inst-RAL = "Atlas Centre, Rutherford Appleton
Laboratory"}
@String{inst-RAL:adr = "Didcot, Oxon, UK"}
@String{inst-U-DUNDEE = "Department of Mathematics and Computer
Science, University of Dundee"}
@String{inst-U-DUNDEE:adr = "Dundee, Scotland"}
@String{inst-U-MANCHESTER = "University of Manchester"}
@String{inst-U-MANCHESTER:adr = "Manchester, England"}
@String{inst-UNIV-WATERLOO = "University of Waterloo"}
@String{inst-UNIV-WATERLOO:adr = "Waterloo, ON, Canada"}
@String{inst-UTK-CS = "Department of Computer Science, University
of Tennessee, Knoxville"}
@String{inst-UTK-CS:adr = "Knoxville, TN 37996, USA"}
@String{j-ACTA-NUMERICA = "Acta Numerica"}
@String{j-BIT = "BIT"}
@String{j-BIT-NUM-MATH = "BIT Numerical Mathematics"}
@String{j-BULL-AMS = "Bulletin of the American Mathematical Society"}
@String{j-BULL-LOND-MATH-SOC = "Bulletin of the London Mathematical Society"}
@String{j-CCPE = "Concurrency and Computation: Prac\-tice and
Experience"}
@String{j-COMPUT-STAT-DATA-ANAL = "Computational Statistics \& Data Analysis"}
@String{j-IEEE-COMPUT-SCI-ENG = "IEEE Computational Science \& Engineering"}
@String{j-IJHPCA = "The International Journal of High Performance
Computing Applications"}
@String{j-IMA-BULL = "IMA Bulletin"}
@String{j-IMA-J-NUMER-ANAL = "IMA Journal of Numerical Analysis"}
@String{j-IMA-NUM-ANA-NEWSLETTER = "IMA Numerical Analysis Newsletter"}
@String{j-INT-J-NUMER-METHODS-ENG = "International Journal for Numerical Methods
in Engineering"}
@String{j-J-COMPLEX-NETWORKS = "Journal of Complex Networks"}
@String{j-J-FLUID-MECH = "Journal of Fluid Mechanics"}
@String{j-LECT-NOTES-COMP-SCI = "Lecture Notes in Computer Science"}
@String{j-LINEAR-ALGEBRA-APPL = "Linear Algebra and Appl."}
@String{j-MATH-COMPUT = "Math. Comp."}
@String{j-MATH-GAZ = "Mathematical Gazette"}
@String{j-MATH-TODAY = "Mathematics Today"}
@String{j-NA-DIGEST = "NA Digest"}
@String{j-NUM-LIN-ALG-APPL = "Numerical Linear Algebra with Applications"}
@String{j-NUM-MATH = "Numer. Math."}
@String{j-NUMER-ALGORITHMS = "Numerical Algorithms"}
@String{j-PARALLEL-COMPUTING = "Parallel Computing"}
@String{j-PHILOS-TRANS-R-SOC-LOND-SER-A = "Philosophical transactions of the
Royal Society of London Series A"}
@String{j-PROC-R-SOC-LOND-SER-A = "Proceedings of the Royal Society of London.
Series A"}
@String{j-R-SOC-OPEN-SCI = "Royal Society Open Science"}
@String{j-SIAM-J-MAT-ANA-APPL = "SIAM J. Matrix Anal. Appl."}
@String{j-SIAM-J-NUMER-ANAL = "SIAM Journal on Numerical Analysis"}
@String{j-SIAM-J-SCI-COMP = "SIAM Journal on Scientific Computing"}
@String{j-SIAM-J-SCI-STAT-COMP = "SIAM Journal on Scientific and Statistical
Computing"}
@String{j-SIAM-NEWS = "SIAM News"}
@String{j-SIAM-REVIEW = "SIAM Review"}
@String{j-TOMS = "ACM Trans. Math. Software"}
@String{pub-ACM = "ACM Press"}
@String{pub-ACM:adr = "New York, NY 10036, USA"}
@String{pub-AMS = "American Mathematical Society"}
@String{pub-AMS:adr = "Providence, RI, USA"}
@String{pub-AP = "Academic Press"}
@String{pub-AW-LONGMAN = "Ad{\-d}i{\-s}on-Wes{\-l}ey Longman"}
@String{pub-AW-LONGMAN:adr = "Reading, MA, USA"}
@String{pub-CH = "Chapman and Hall"}
@String{pub-CH:adr-L = "London"}
@String{pub-CHAPMAN-HALL-CRC = "Chapman and Hall/CRC"}
@String{pub-CHAPMAN-HALL-CRC:adr = "Boca Raton, FL, USA"}
@String{pub-ELS = "Elsevier Science Publishers B.V."}
@String{pub-ELS:adr = "Amsterdam, The Netherlands"}
@String{pub-IEEE = "IEEE Computer Society Press"}
@String{pub-IEEE:adr = "1109 Spring Street, Suite 300,
Silver Spring, MD 20910, USA"}
@String{pub-LONGMAN-ST = "Longman Scientific and Technical"}
@String{pub-LONGMAN-ST:adr = "Essex, UK"}
@String{pub-KLUWER = "Kluwer Academic Publishers"}
@String{pub-KLUWER:adr = "Norwell, MA, USA, and Dordrecht, The
Netherlands"}
@String{pub-OXFORD = "Oxford University Press"}
@String{pub-OXFORD:adr = "Walton Street, Oxford OX2 6DP, UK"}
@String{pub-PENGUIN = "Penguin"}
@String{pub-PENGUIN:adr-H = "Harmondsworth, UK"}
@String{pub-PENGUIN:adr-L = "London"}
@String{pub-PENGUIN:adr-NY = "New York"}
@String{pub-PRINCETON = "Princeton University Press"}
@String{pub-PRINCETON:adr = "Princeton, NJ, USA"}
@String{pub-SIAM = "Society for Industrial and Applied
Mathematics"}
@String{pub-SIAM:adr = "Philadelphia, PA, USA"}
@String{pub-SPRINGER = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SPRINGER:adr-B = "Berlin"}
@String{pub-SPRINGER:adr-NY = "New York"}
@String{pub-SV = "Springer-Verlag"}
@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg, Germany~/
London, UK~/ etc."}
@String{pub-WORLD-SCI = "World Scientific Publishing Co."}
@String{pub-WORLD-SCI:adr = "Singapore; Philadelphia, PA, USA; River
Edge, NJ, USA"}
@MastersThesis{Higham:1983:MCN,
author = "N. J. Higham",
title = "Matrix Condition Numbers",
type = "{M.Sc. Thesis}",
school = inst-U-MANCHESTER,
address = inst-U-MANCHESTER:adr,
pages = "iv + 86",
month = oct,
year = "1983",
bibdate = "Tue Mar 21 16:29:28 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@TechReport{Higham:1983:UBC,
author = "Nicholas J. Higham",
title = "Upper bounds for the condition number of a triangular
matrix",
type = "Numerical Analysis Report",
number = "86",
institution = inst-U-MANCHESTER,
address = inst-U-MANCHESTER:adr,
month = may,
year = "1983",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@TechReport{Higham:1985:MCB,
author = "Nicholas J. Higham",
title = "Matrix Computations in {Basic} on a Microcomputer",
type = "Numerical Analysis Report",
number = "101",
institution = "Department of Mathematics, University of Manchester",
address = "Manchester, M13 9PL, UK",
pages = "62",
month = jun,
year = "1985",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
created = "2013.10.02",
updated = "2013.10.02",
}
@PhdThesis{Higham:1985:NPN,
author = "Nicholas J. Higham",
title = "Nearness Problems in Numerical Linear Algebra",
school = inst-U-MANCHESTER,
address = inst-U-MANCHESTER:adr,
pages = "173",
month = jul,
year = "1985",
bibdate = "Tue Mar 21 16:29:32 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@Article{Higham:1986:CPD,
author = "Nicholas J. Higham",
title = "Computing the Polar Decomposition---with
Applications",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "7",
number = "4",
pages = "1160--1174",
month = oct,
year = "1986",
CODEN = "SIJCD4",
ISSN = "0196-5204",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
mynote = "N.A. Report 94, November 1984. (Proof in Appendix is
not in paper).",
}
@Article{Higham:1986:EAC,
author = "Nicholas J. Higham",
title = "Efficient Algorithms for Computing the Condition
Number of a Tridiagonal Matrix",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "7",
number = "1",
pages = "150--165",
year = "1986",
CODEN = "SIJCD4",
ISSN = "0196-5204",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
}
@Article{Higham:1986:MCB,
author = "Nicholas J. Higham",
title = "Matrix Computations in {Basic} on a Microcomputer",
journal = j-IMA-BULL,
volume = "22",
pages = "13--20",
year = "1986",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "IMA Bulletin",
}
@Article{Higham:1986:NMM,
author = "Nicholas J. Higham",
title = "{Newton}'s Method for the Matrix Square Root",
journal = j-MATH-COMPUT,
volume = "46",
number = "174",
pages = "537--549",
month = apr,
year = "1986",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F30 (65H10)",
MRnumber = "87d:65045",
MRreviewer = "Lars Eld{\'e}n",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
JSTOR database; Theory/Matrix.bib",
acknowledgement = ack-njh,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Dept. of Math., Manchester Univ., UK",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "equation; iterative methods; mathematical convergence;
matrix algebra; matrix square root; Newton iteration;
Newton method; perturbation analysis; properties;
quadratic matrix",
kwds = "nla, matrix function, matrix square root, Newton's
method",
treatment = "T Theoretical or Mathematical",
}
@Article{Higham:1987:CRS,
author = "Nicholas J. Higham",
title = "Computing Real Square Roots of a Real Matrix",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88/89",
pages = "405--430",
year = "1987",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:1987:EAB,
author = "Nicholas J. Higham",
title = "Error Analysis of the {Bj{\"o}rck}-{Pereyra}
Algorithms for Solving {Vandermonde} Systems",
journal = j-NUM-MATH,
volume = "50",
number = "5",
pages = "613--632",
year = "1987",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@InProceedings{Higham:1987:NLA,
author = "N. J. Higham and G. W. Stewart",
title = "Numerical Linear Algebra in Statistical Computing",
crossref = "Iserles:1987:SAN",
pages = "41--57",
year = "1987",
bibdate = "Thu May 29 17:14:49 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib",
acknowledgement = ack-nhfb,
xxpages = "41--58",
}
@Article{Higham:1987:SCN,
author = "Nicholas J. Higham",
title = "A Survey of Condition Number Estimation for Triangular
Matrices",
journal = j-SIAM-REVIEW,
volume = "29",
number = "4",
pages = "575--596",
month = dec,
year = "1987",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1029112",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65F35",
MRnumber = "88j:65086",
bibdate = "Sat Mar 29 09:54:19 MDT 2014",
bibsource = "Compendex database;
http://epubs.siam.org/toc/siread/29/4;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
abstract = "We survey and compare a wide variety of techniques for
estimating the condition number of a triangular matrix,
and make recommendations concerning the use of the
estimates in applications. Each of the methods is shown
to bound the condition number; the bounds can broadly
be categorised as upper bounds from matrix theory and
lower bounds from heuristic or probabilistic
algorithms. For each bound we examine by how much, at
worst, it can overestimate or underestimate the
condition number. Numerical experiments are presented
in order to illustrate and compare the practical
performance of the condition estimators.",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ of Manchester, Manchester, Engl",
classification = "723; 921",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "computer programming --- Algorithms; condition number
estimation; mathematical techniques; Matrix Algebra;
matrix condition number; qr decomposition; rank
estimation; triangular matrices",
onlinedate = "December 1987",
}
@Article{Higham:1988:AFC,
author = "Nicholas J. Higham",
title = "Algorithm 674: {FORTRAN} Codes for Estimating the
One-Norm of a Real or Complex Matrix, with Applications
to Condition Estimation",
journal = j-TOMS,
volume = "14",
number = "4",
pages = "381--396",
month = dec,
year = "1988",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65-04 (65F35)",
MRnumber = "1 062 484",
bibdate = "Sat Aug 27 15:05:32 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "See also \cite{Higham:1989:CFC}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p381-higham/;
http://www.acm.org/pubs/toc/Abstracts/0098-3500/214386.html",
abstract = "FORTRAN 77 codes SONEST and CONEST are presented for
estimating the 1-norm ( or the infinity-norm) of a real
or complex matrix, respectively. The codes are of wide
applicability in condition estimation since explicit
access to the matrix, $A$, is not required; instead,
matrix-vector products $ A x $ and $ A^T x $ are
computed by the calling program via a reverse
communication interface. The algorithms are based on a
convex optimization method for estimating the 1-norm of
a real matrix devised by Hager. We derive new results
concerning the behavior of Hager's method, extend it to
complex matrices, and make several algorithmic
modifications in order to improve the reliability and
efficiency.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
keywords = "algorithms; condition estimation; nla; software, nla,
condition estimation, software",
subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra.",
}
@Article{Higham:1988:CNS,
author = "Nicholas J. Higham",
title = "Computing a Nearest Symmetric Positive Semidefinite
Matrix",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "103",
pages = "103--118",
year = "1988",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:1988:FSV,
author = "Nicholas J. Higham",
title = "Fast Solution of {Vandermonde}-like Systems Involving
Orthogonal Polynomials",
journal = j-IMA-J-NUMER-ANAL,
volume = "8",
number = "4",
pages = "473--486",
month = oct,
year = "1988",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/8.4.473",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65H10 (65F30)",
MRnumber = "89k:65067",
bibdate = "Thu Aug 25 10:58:30 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
MathSciNet database",
abstract = "Consider the $ (n + 1) \times (n + 1) $
Vandermonde-like matrix $ P = [{pi - 1}(\alpha_{j -
1})] $, where the polynomials $ p_0 (x), \ldots {},
p_n(x) $ satisfy a three-term recurrence relation. We
develop algorithms for solving the primal and dual
systems, $ P x = b $ and $ P^T a = f $ respectively, in
$ O(n^2) $ arithmetic operations and $ O(n) $ elements
of storage. These algorithms generalize those of
Bj{\"o}rck \& Pereyra which apply to the monomial case
$ p_i(x) $. When the $ p_i(x) $ are the Chebyshev
polynomials, the algorithms are shown to be numerically
unstable. However, it is found empirically that the
addition of just one step of iterative refinement is,
in single precision, enough to make the algorithms
numerically stable.",
acknowledgement = ack-nhfb # " and " # ack-njh,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Higham:1988:SPP,
author = "Nicholas J. Higham",
title = "The Symmetric {Procrustes} Problem",
journal = j-BIT,
volume = "28",
number = "1",
pages = "133--143",
year = "1988",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F20 (41A29 73K05)",
MRnumber = "89g:65047",
MRreviewer = "N. Gass",
bibdate = "Thu Nov 12 18:12:56 MST 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh # " and " # ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Higham:1989:AST,
author = "Nicholas J. Higham",
title = "The Accuracy of Solutions to Triangular Systems",
journal = j-SIAM-J-NUMER-ANAL,
volume = "26",
number = "5",
pages = "1252--1265",
month = oct,
year = "1989",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F05 (65G05)",
MRnumber = "90i:65053",
MRreviewer = "James Weldon Demmel",
bibdate = "Mon Jan 20 15:27:00 MST 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Higham:1989:CFC,
author = "Nicholas J. Higham",
title = "Corrigendum: ``{Algorithm} 674: {FORTRAN} Codes for
Estimating the One-Norm of a Real or Complex Matrix,
with Applications to Condition Estimation''",
journal = j-TOMS,
volume = "15",
number = "2",
pages = "168--168",
month = jun,
year = "1989",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Sep 30 01:18:49 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "See \cite{Higham:1988:AFC}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p168-higham/;
http://www.acm.org/pubs/toc/Abstracts/0098-3500/214391.html",
abstract = "We omitted giving this article an ACM algorithm number
when it was first published in its entirety in the
December 1988 issue of {\em TOMS}, Vol. 14, No. 4, pp.
381-396. To correct this, we do so here, and reprint
the title as a pointer to the original article.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
keywords = "algorithms",
subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra.",
}
@TechReport{Higham:1989:CTM,
author = "Nicholas J. Higham",
title = "A Collection of Test Matrices in {MATLAB}",
type = "Numerical Analysis Report",
number = "172",
institution = inst-U-MANCHESTER,
address = inst-U-MANCHESTER:adr,
month = jul,
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
mynote = "Published version: \cite{Higham:1991:ACT}.",
}
@Article{Higham:1989:LGF,
author = "Nicholas J. Higham and Desmond J. Higham",
title = "Large Growth Factors in {Gaussian} Elimination with
Pivoting",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "10",
number = "2",
pages = "155--164",
month = apr,
year = "1989",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:1989:MCP,
author = "Nicholas J. Higham",
title = "Matrix Computations on a {PC}",
journal = j-SIAM-NEWS,
volume = "22",
pages = "16",
month = jan,
year = "1989",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@InProceedings{Higham:1989:MNP,
author = "Nicholas J. Higham",
editor = "M. J. C. Gover and S. Barnett",
booktitle = "Applications of Matrix Theory",
title = "Matrix Nearness Problems and Applications",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "1--27",
year = "1989",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@TechReport{Demmel:1990:IEB,
author = "J. Demmel and N. Higham",
title = "Improved Error Bounds for Underdetermined System
Solvers",
type = "LAPACK Working Note",
number = "23",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = aug,
year = "1990",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-90-113, August 1990.",
URL = "http://www.netlib.org/lapack/lawns/lawn23.ps;
http://www.netlib.org/lapack/lawnspdf/lawn23.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Demmel:1990:SBA,
author = "J. Demmel and N. Higham",
title = "Stability of Block Algorithms with Fast Level 3
{BLAS}",
type = "LAPACK Working Note",
number = "22",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = jul,
year = "1990",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-90-110, July 1990.",
URL = "http://www.netlib.org/lapack/lawns/lawn22.ps;
http://www.netlib.org/lapack/lawnspdf/lawn22.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{DuCroz:1990:SMM,
author = "J. {Du Croz} and N. Higham",
title = "Stability of Methods for Matrix Inversion",
type = "LAPACK Working Note",
number = "27",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = oct,
year = "1990",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-90-119, October, 1990.",
URL = "http://www.netlib.org/lapack/lawns/lawn27.ps;
http://www.netlib.org/lapack/lawnspdf/lawn27.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Higham:1990:ACD,
author = "Nicholas J. Higham",
editor = "M. G. Cox and S. J. Hammarling",
booktitle = "Reliable Numerical Computation",
title = "Analysis of the {Cholesky} Decomposition of a
Semi-definite Matrix",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "161--185",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@Article{Higham:1990:BEG,
author = "Nicholas J. Higham",
title = "Bounding the Error in {Gaussian} Elimination for
Tridiagonal Systems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "11",
number = "4",
pages = "521--530",
month = oct,
year = "1990",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Higham:1990:CEB,
author = "Nicholas J. Higham",
editor = "Philip J. Brown and Wayne A. Fuller",
booktitle = "Statistical Analysis of Measurement Error Models and
Applications, Contemporary Mathematics 112",
title = "Computing Error Bounds for Regression Problems",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "195--208",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@Article{Higham:1990:EFM,
author = "Nicholas J. Higham",
title = "Exploiting Fast Matrix Multiplication Within the Level
3 {BLAS}",
journal = j-TOMS,
volume = "16",
number = "4",
pages = "352--368",
month = dec,
year = "1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65-04 (65F99)",
MRnumber = "1 095 133",
bibdate = "Sun Sep 04 23:21:57 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Describes algorithms based on Strassen's method which
are asymptotically faster than the standard $ {N}^3 $
algorithm, and in practice, faster for $ {N} \approx
100 $, and examines their numerical stability. See
\cite{Dongarra:1990:ASL,Demmel:1992:SBA}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p352-higham/",
abstract = "The Level 3 BLAS (BLAS3) are a set of specifications
of FORTRAN 77 subprograms for carrying out matrix
multiplications and the solution of triangular systems
with multiple right-hand sides. They are intended to
provide efficient and portable building blocks for
linear algebra algorithms on high-performance
computers. We describe algorithms for the BLAS3
operations that are asymptotically faster than the
conventional ones. These algorithms are based on
Strassen's method for fast matrix multiplication, which
is now recognized to be a practically useful technique
once matrix dimensions exceed about 100. We pay
particular attention to the numerical stability of
these ``fast BLAS3.'' Error bounds are given and their
significance is explained and illustrated with the aid
of numerical experiments. Our conclusion is that the
fast BLAS3, although not as strongly stable as
conventional implementations, are stable enough to
merit careful consideration in many applications.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
keywords = "algorithms",
subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra. {\bf D.3.2}:
Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN 77.",
}
@Article{Higham:1990:EMN,
author = "Nicholas J. Higham",
title = "Experience with a Matrix Norm Estimator",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "11",
number = "4",
pages = "804--809",
month = jul,
year = "1990",
CODEN = "SIJCD4",
ISSN = "0196-5204",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
mynote = "Timely Communication.",
}
@Article{Higham:1990:FMM,
author = "Nicholas J. Higham",
title = "Is Fast Matrix Multiplication of Practical Use?",
journal = j-SIAM-NEWS,
volume = "23",
pages = "12--??",
month = nov,
year = "1990",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Article{Higham:1990:FPD,
author = "Nicholas J. Higham and Robert S. Schreiber",
title = "Fast Polar Decomposition of an Arbitrary Matrix",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "11",
number = "4",
pages = "648--655",
month = jul,
year = "1990",
CODEN = "SIJCD4",
ISSN = "0196-5204",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
annote = "Prepublished as RIACS technical report 88.29 and NASA
Contractor Report 185412.",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
}
@InProceedings{Higham:1990:HAG,
author = "Nicholas J. Higham",
editor = "D. F. Griffiths and G. A. Watson",
booktitle = "Numerical Analysis 1989, Proceedings of the 13th
Dundee Conference",
title = "How Accurate is {Gaussian} Elimination?",
volume = "228",
publisher = pub-LONGMAN-ST,
address = pub-LONGMAN-ST:adr,
pages = "137--154",
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
series = "Pitman Research Notes in Mathematics",
acknowledgement = ack-njh,
}
@TechReport{Higham:1990:IRE,
author = "Nicholas J. Higham",
title = "Iterative Refinement Enhances the Stability of {$ Q R
$} Factorization Methods for Solving Linear Equations",
type = "Numerical Analysis Report",
number = "182",
institution = inst-U-MANCHESTER,
address = inst-U-MANCHESTER:adr,
month = apr,
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
mynote = "Contains proofs in the appendix that are not in
\cite{Higham:1991:IRE}.",
}
@Article{Higham:1990:RGH,
author = "Nicholas J. Higham",
title = "Review of {``G. H. Golub and C. F. Van Loan, Matrix
Computations, Second Edition, Johns Hopkins University
Press, Baltimore, Maryland, 1989''}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "141",
pages = "289--292",
year = "1990",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:1990:RMJ,
author = "Nicholas J. Higham",
title = "Review of {``M. J. C. Gover and S. Barnett, eds.,
Applications of Matrix Theory, Oxford University Press,
1989''}",
journal = j-MATH-GAZ,
volume = "74",
number = "468",
pages = "202",
year = "1990",
CODEN = "MAGAAS",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}
@Article{Higham:1990:SAA,
author = "Nicholas J. Higham",
title = "Stability Analysis of Algorithms for Solving Confluent
{Vandermonde}-like Systems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "11",
number = "1",
pages = "23--41",
month = jan,
year = "1990",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:1991:ACT,
author = "Nicholas J. Higham",
title = "Algorithm 694: {A} Collection of Test Matrices in
{MATLAB}",
journal = j-TOMS,
volume = "17",
number = "3",
pages = "289--305",
month = sep,
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 23:52:04 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p289-higham/",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
keywords = "algorithms; experimentation; performance; theory",
subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra.",
}
@Article{Higham:1991:IRE,
author = "Nicholas J. Higham",
title = "Iterative Refinement Enhances the Stability of {$ Q R
$} Factorization Methods for Solving Linear Equations",
journal = j-BIT,
volume = "31",
number = "3",
pages = "447--468",
year = "1991",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F05 (65F10 65G05)",
MRnumber = "92h:65043",
MRreviewer = "James Weldon Demmel",
bibdate = "Fri Nov 13 07:00:34 MST 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh # " and " # ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@InCollection{Higham:1991:SLE,
author = "Nicholas J. Higham",
editor = "Christine Bondi",
booktitle = "New Applications of Mathematics",
title = "Solving Linear Equations",
publisher = pub-PENGUIN,
address = pub-PENGUIN:adr-L,
pages = "33--56",
year = "1991",
MRclass = "65-01",
MRnumber = "1190077",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
mynote = "Chapter 2.",
}
@Article{Higham:1991:TMP,
author = "Nicholas J. Higham",
title = "Three Measures of Precision in Floating Point
Arithmetic",
journal = j-NA-DIGEST,
volume = "91",
number = "16",
year = "1991",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Electronic mail magazine:
\path|na.help@na-net.ornl.gov|.",
acknowledgement = ack-njh,
fjournal = "NA Digest",
mynote = "Sunday, April 21, 1991.",
}
@TechReport{Demmel:1992:BLF,
author = "James Demmel and Nick Higham and Rob Schreiber",
title = "Block {LU} Factorization",
type = "LAPACK Working Note",
number = "40",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = feb,
year = "1992",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-92-149, February 1992.",
URL = "http://www.netlib.org/lapack/lawns/lawn40.ps;
http://www.netlib.org/lapack/lawnspdf/lawn40.pdf",
acknowledgement = ack-nhfb,
}
@Article{Demmel:1992:SBA,
author = "James W. Demmel and Nicholas J. Higham",
title = "Stability of Block Algorithms with Fast Level-3
{BLAS}",
journal = j-TOMS,
volume = "18",
number = "3",
pages = "274--291",
month = sep,
year = "1992",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Sep 30 01:27:16 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "See
\cite{Dongarra:1990:ASL,Higham:1990:EFM,Dayde:1994:PBI}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p274-demmel/",
abstract = "Block algorithms are becoming increasingly popular in
matrix computations. Since their basic unit of data is
a submatrix rather than a scalar, they have a higher
level of granularity than point algorithms, and this
makes them well suited to high-performance computers.
The numerical stability of the block algorithms in the
new linear algebra program library LAPACK is
investigated here. It is shown that these algorithms
have backward error analyses in which the backward
error bounds are commensurate with the error bounds for
the underlying level-3 BLAS (BLAS3). One implication is
that the block algorithms are as stable as the
corresponding point algorithms when conventional BLAS3
are used. A second implication is that the use of BLAS3
based on fast matrix multiplication techniques affects
the stability only insofar as it increases the constant
terms in the normwise backward error bounds. For linear
equation solvers employing {\em LU} factorization, it
is shown that fixed precision iterative refinement
helps to mitigate the effect of the larger error
constants. Despite the positive results presented here,
not all plausible block algorithms are stable; we
illustrate this with the example of {\em LU}
factorization with block triangular factors and
describe how to check a block algorithm for stability
without doing a full error analysis.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
keywords = "algorithms; performance",
subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
ANALYSIS, Numerical Linear Algebra. {\bf F.2.1}: Theory
of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices.",
}
@Article{DuCroz:1992:SMM,
author = "Jeremy J. {Du Croz} and Nicholas J. Higham",
title = "Stability of Methods for Matrix Inversion",
journal = j-IMA-J-NUMER-ANAL,
volume = "12",
number = "1",
pages = "1--19",
year = "1992",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/12.1.1",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65F05",
MRnumber = "92k:65047",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
MathSciNet database",
abstract = "Inversion of a triangular matrix can be accomplished
in several ways. The standard methods are characterized
by the loop ordering, whether matrix-vector
multiplication, solution of a triangular system, or a
rank-1 update is done inside the outer loop, and
whether the method is blocked or unblocked. The
numerical stability properties of these methods are
investigated. It is shown that unblocked methods
satisfy pleasing bounds on the left or right residual.
However, for one of the block methods it is necessary
to convert a matrix multiplication into the solution of
a multiple right-hand side triangular system in order
to have an acceptable residual bound. The inversion of
a full matrix given a factorization PA=LU is also
considered, including the special cases of symmetric
indefinite and symmetric positive definite matrices.
Three popular methods are shown to possess satisfactory
residual bounds, subject to a certain requirement on
the implementation, and an attractive new method is
described. This work was motivated by the question of
what inversion methods should be used in LAPACK.",
acknowledgement = ack-nhfb # " and " # ack-njh,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Higham:1992:BEC,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "Backward Error and Condition of Structured Linear
Systems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "1",
pages = "162--175",
month = jan,
year = "1992",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:1992:CPT,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "Componentwise Perturbation Theory for Linear Systems
with Multiple Right-Hand Sides",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "174",
pages = "111--129",
year = "1992",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:1992:EMN,
author = "Nicholas J. Higham",
title = "Estimating the Matrix {$p$}-norm",
journal = j-NUM-MATH,
volume = "62",
pages = "539--555",
year = "1992",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Higham:1992:IWP,
author = "Nicholas J. Higham",
title = "{IMA} Workshop Participants {F}{\^e}te {Golub} on 60th
Birthday",
journal = j-SIAM-NEWS,
volume = "25",
pages = "3--??",
month = may,
year = "1992",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Article{Higham:1992:JAF,
author = "Nicholas J. Higham",
title = "The Joy of Anonymous {FTP}",
journal = j-IMA-NUM-ANA-NEWSLETTER,
volume = "17",
number = "1",
pages = "61--64",
month = oct,
year = "1992",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "IMA Numerical Analysis Newsletter",
}
@Article{Higham:1992:LRM,
author = "Nicholas J. Higham",
title = "{LAPACK} Released in {March}",
journal = j-SIAM-NEWS,
volume = "25",
pages = "20",
month = may,
year = "1992",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@TechReport{Higham:1992:PTB,
author = "Nick Higham",
title = "Perturbation Theory and Backward Error for {$ A X - X
B = C $}",
type = "LAPACK Working Note",
number = "42",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = apr,
year = "1992",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-92-153, April, 1992.",
URL = "http://www.netlib.org/lapack/lawns/lawn42.ps;
http://www.netlib.org/lapack/lawnspdf/lawn42.pdf",
acknowledgement = ack-nhfb,
}
@Article{Higham:1992:SMM,
author = "Nicholas J. Higham",
title = "Stability of a Method for Multiplying Complex Matrices
with Three Real Matrix Multiplications",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "3",
pages = "681--687",
month = jul,
year = "1992",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@TechReport{Balle:1993:STM,
author = "Susanne M. Balle and Per Christian Hansen and Nicholas
J. Higham",
title = "A {Strassen}-Type Matrix Inversion Algorithm for the
{Connection Machine}",
number = "CNC/1993/028",
institution = "Centre for Novel Computing, " # inst-U-MANCHESTER,
address = inst-U-MANCHESTER:adr,
type = "Technical Report",
pages = "29",
month = oct,
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@Article{Demmel:1993:IEB,
author = "James W. Demmel and Nicholas J. Higham",
title = "Improved Error Bounds for Underdetermined System
Solvers",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "14",
number = "1",
pages = "1--14",
month = jan,
year = "1993",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
mynote = "Also LAPACK Working Note \#23.",
}
@Article{Hammarling:1993:CHW,
author = "Sven Hammarling and Nicholas J. Higham and Bo
K{\aa}gstr{\"o}m",
title = "{CERFACS} Hosts Workshop on Reliability of
Computations",
journal = j-SIAM-NEWS,
volume = "26",
pages = "4",
month = jul,
year = "1993",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Article{Higham:1993:AFP,
author = "Nicholas J. Higham",
title = "The accuracy of floating point summation",
journal = j-SIAM-J-SCI-COMP,
volume = "14",
number = "4",
pages = "783--799",
month = jul,
year = "1993",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/0914050",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65G05 (65B10)",
MRnumber = "94a:65025",
bibdate = "Thu Aug 23 06:36:53 2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://citeseer.nj.nec.com/higham93accuracy.html;
http://citeseer.nj.nec.com/rd/4651150%2C296147%2C1%2C0.25%2CDownload/http%253A%252F%252Fciteseer.nj.nec.com/cache/papers2/cs/14280/http%253AzSzzSzwww.maths.man.ac.ukzSz%257EnareportszSznarep198.pdf/higham93accuracy.pdf;
http://citeseer.nj.nec.com/rd/4651150%2C296147%2C1%2C0.25%2CDownload/http%253A%252F%252Fwww.maths.man.ac.uk/%257Enareports/narep198.ps.gz",
abstract = "The usual recursive summation technique is just one of
several ways of computing the sum of $n$ floating point
numbers. Five summation methods and their variations
are analyzed. The accuracy of the methods is compared
using rounding error analysis and numerical
experiments. Four of the methods are shown to be
special cases of a general class of methods, and an
error analysis is given for this class. No one method
is uniformly more accurate than the others, but some
guidelines are given on the choice of method in
particular cases.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Manchester Univ., UK",
classification = "C4110 (Error analysis in numerical methods); C5230
(Digital arithmetic methods)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "Floating point numbers; Floating point summation;
Numerical experiments; Recursive summation technique;
Rounding error analysis",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Error analysis",
}
@InCollection{Higham:1993:CCL,
author = "Nicholas J. Higham",
editor = "M. Chu and others",
booktitle = "The {Lanczos} Collected Papers with Commentaries",
title = "{Commentary on C. Lanczos, ``Introduction'' to
``Tables of Chebyshev Polynomials $ S_n(x) $ and $
C_n(x) $'', Nat.\ Bur.\ Stand., Appl.\ Math.\ Series 9,
1952, v--xxvi}",
publisher = "????",
address = "????",
year = "1993",
bibdate = "Wed Nov 1 08:00:18 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear.",
acknowledgement = ack-njh,
}
@InProceedings{Higham:1993:CEA,
author = "Nicholas J. Higham and Philip A. Knight",
title = "Componentwise Error Analysis for Stationary Iterative
Methods",
crossref = "Meyer:1993:LAM",
pages = "29--46",
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
series = "IMA Volumes in Mathematics and its Applications",
acknowledgement = ack-njh,
}
@Article{Higham:1993:FPB,
author = "Nicholas J. Higham and Philip A. Knight",
title = "Finite Precision Behavior of Stationary Iteration for
Solving Singular Systems",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "192",
pages = "165--186",
year = "1993",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
mynote = "Special issue for Proceedings of Workshop on
Computational Linear Algebra in Algebraic and Related
Problems.",
}
@Book{Higham:1993:HWM,
author = "Nicholas J. Higham",
title = "Handbook of Writing for the Mathematical Sciences",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xii + 241",
month = jun,
year = "1993",
ISBN = "0-89871-314-5",
ISBN-13 = "978-0-89871-314-5",
LCCN = "QA42.H54 1993",
bibdate = "Tue Mar 1 12:03:19 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
http://www.math.utah.edu/pub/tex/bib/texbook3.bib",
price = "US\$21.50",
acknowledgement = ack-njh,
note-1 = "[From the publisher]: Having trouble with your latest
math paper? Giving a presentation that you just can't
pull together? Struggling with your thesis or trying to
get your first article published in a technical
journal? Handbook of Writing for the Mathematical
Sciences is the book for you!
This handy volume provides information on virtually
every issue you will face when writing a technical
paper or talk, from choosing the right journal to
handling your references. You'll also get an overview
of the entire publication process--invaluable for
anyone hoping to publish in a technical journal.",
note-2 = "To write a truly impressive paper, you'll need to
understand the anatomy of a research paper and the
steps involved in revising a draft. This book offers
discussions of these fundamental topics, along with
illustrative and provocative examples. Also included
are chapters on standard English usage, using computers
for writing and research, and writing technical
material when English is a foreign language.
This handbook provides much-needed advice on handling
the basic ingredients of a research paper, like
definitions, theorems, examples, and equations. In
addition, appendices provide essential reference
material, including summaries of \LaTeX{} symbols and
Emacs commands, addresses of mathematical societies,
and a list of papers that have won expository writing
prizes.",
note-3 = "This book is ideal for graduate students and teachers.
Among its special features:
\begin{itemize} \item Detail and extensive use of
examples make it an excellent teaching tool
\item Discusses \TeX{} and other software tools for
preparing publications
\item Thorough treatment, with examples, of how to
write slides (transparencies) for a mathematical
talk.
\item Comprehensive index and extensive bibliography
make it an excellent reference
\item Readable for everyone in the field--from
undergraduates to seasoned professionals
\end{itemize}",
note-4 = "About the Author: Nicholas J. Higham is a Reader in
Mathematics at the University of Manchester, UK. He is
the author of more than 40 publications and is a member
of the editorial board of the SIAM Journal on Matrix
Analysis and Applications.",
tableofcontents = "Preface \\
1: General Principles \\
2: Writer's Tools and Recommended Reading \\
3: Mathematical Writing \\
4: English Usage \\
5: When English is a Foreign Language \\
6: Writing a Paper \\
7: Revising a Draft \\
8: Publishing a Paper \\
9: Writing a Talk \\
10: Computer Aids for Writing and Research \\
Appendix A: The Greek Alphabet \\
Appendix B: Summary of \TeX{} and \LaTeX{} Symbols \\
Appendix C: GNU Emacs--The Sixty+ Most Useful Commands;
\\
Appendix D: Mathematical Organizations in the UK and
USA \\
Appendix E: Winners of Prizes for Expository Writing;
\\
Appendix F: Glossary \\
Bibliography \\
Index",
}
@Article{Higham:1993:ODS,
author = "Nicholas J. Higham",
title = "Optimization by Direct Search in Matrix Computations",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "14",
number = "2",
pages = "317--333",
month = apr,
year = "1993",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@TechReport{Higham:1993:PSV,
author = "Nicholas J. Higham and Pythagoras Papadimitriou",
title = "Parallel Singular Value Decomposition via the Polar
Decomposition",
type = "Numerical Analysis Report",
number = "239",
institution = inst-MCCM,
address = inst-MCCM:adr,
month = oct,
year = "1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
mynote = "Longer version of \cite{Higham:1994:PAC}.",
}
@InProceedings{Higham:1993:PTBa,
author = "Nicholas J. Higham",
title = "Perturbation theory and backward error for {$ A X - X
B = C $}",
crossref = "Moonen:1993:LAL",
pages = "391--392",
year = "1993",
bibdate = "Thu May 29 18:39:54 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
}
@Article{Higham:1993:PTBb,
author = "Nicholas J. Higham",
title = "Perturbation theory and backward error analysis for {$
A X - X B = C $}",
journal = j-BIT,
volume = "33",
number = "1",
pages = "124--136",
year = "1993",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F05 (65G05)",
MRnumber = "96a:65036",
bibdate = "Fri Nov 13 07:00:34 MST 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit33.html",
acknowledgement = ack-njh # " and " # ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@TechReport{Higham:1993:TMT,
author = "Nicholas J. Higham",
title = "The {Test Matrix Toolbox} for {Matlab}",
type = "Numerical Analysis Report",
number = "237",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "76",
month = dec,
year = "1993",
bibdate = "Tue Mar 30 17:06:37 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
abstract-1 = "We describe version 2.0 of the Test Matrix Toolbox for
Matlab 4. The toolbox contains a collection of test
matrices, routines for visualizing matrices, and
miscellaneous routines that provide useful additions to
Matlab's existing set of functions. There are 58
parametrized test matrices, which are mostly square,
dense, nonrandom, and of arbitrary dimension. The test
matrices include ones with known inverses or known
eigenvalues; ill-conditioned or rank deficient
matrices; and symmetric, positive definite, orthogonal,
defective, involutary, and totally positive matrices.",
abstract-2 = "We describe version 2.0 of the Test Matrix Toolbox for
Matlab The visualization routines display surface plots
of a matrix and its (pseudo-) inverse, the field of
values, Gershgorin disks, and two- and
three-dimensional views of pseudospectra. We explain
the need for collections of test matrices and summarize
the features of the collection in the toolbox. We give
examples of the use of the toolbox and explain some of
the interesting properties of the Frank and Pascal
matrices, and of random, magic square and companion
matrices. The leading comment lines from all the
toolbox routines are listed.",
acknowledgement = ack-njh,
keywords = "test matrix, Matlab, pseudospectrum, visualization,
Frank matrix, Pascal matrix, companion matrix, magic
square matrix, random matrix",
}
@Article{Higham:1994:BVT,
author = "Nicholas J. Higham",
title = "{\BibTeX}: {A} Versatile Tool for {\LaTeX} Users",
journal = j-SIAM-NEWS,
volume = "27",
pages = "10, 11, 19",
month = jan,
year = "1994",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Book{Higham:1994:HWM,
author = "Nicholas J. Higham",
title = "Handbook of Writing for the Mathematical Sciences",
publisher = "Nippon Hyoron Sha",
address = "Tokyo",
pages = "x + 235",
year = "1994",
ISBN = "4-535-78211-3",
ISBN-13 = "978-4-535-78211-2",
bibdate = "Wed Sep 28 09:02:11 GMT 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Japanese edition of \cite{Higham:1993:HWM}, translated
by Shoji Okumura and Takemitsu Hasegawa.",
acknowledgement = ack-njh,
}
@Article{Higham:1994:MSD,
author = "Nicholas J. Higham",
title = "The Matrix Sign Decomposition and Its Relation to the
Polar Decomposition",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "212/213",
pages = "3--20",
year = "1994",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Tue Jan 3 12:21:48 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@InProceedings{Higham:1994:NPA,
author = "Nicholas J. Higham and Pythagoras Papadimitriou",
editor = "John G. Lewis",
booktitle = "Proceedings of the Fifth SIAM Conference on Applied
Linear Algebra",
title = "A New Parallel Algorithm for Computing the Singular
Value Decomposition",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "80--84",
year = "1994",
ISBN = "0-89871-336-6",
ISBN-13 = "978-0-89871-336-7",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@Article{Higham:1994:PAC,
author = "Nicholas J. Higham and Pythagoras Papadimitriou",
title = "A Parallel Algorithm for Computing the Polar
Decomposition",
journal = j-PARALLEL-COMPUTING,
volume = "20",
number = "8",
pages = "1161--1173",
month = aug,
year = "1994",
CODEN = "PACOEJ",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
}
@TechReport{Higham:1994:SCPa,
author = "Nicholas J. Higham",
title = "A Survey of Componentwise Perturbation Theory in
Numerical Linear Algebra",
type = "Numerical Analysis Report",
number = "241",
institution = inst-U-MANCHESTER,
address = inst-U-MANCHESTER:adr,
month = feb,
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in Mathematics of Computation 1943--1993, W.
Gautschi, ed. Proceedings of Symposia in Applied
Mathematics, American Mathematical Society.",
acknowledgement = ack-njh,
}
@InProceedings{Higham:1994:SCPb,
author = "Nicholas J. Higham",
editor = "Walter Gautschi",
booktitle = "{Mathematics of Computation} 1943--1993: {A} Half
Century of Computational Mathematics",
title = "A Survey of Componentwise Perturbation Theory in
Numerical Linear Algebra",
volume = "48",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "49--77",
year = "1994",
bibdate = "Fri Mar 24 08:51:18 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
series = "Proceedings of Symposia in Applied Mathematics",
acknowledgement = ack-njh,
}
@Article{Higham:1994:SPI,
author = "Nicholas J. Higham and Alex Pothen",
title = "Stability of the Partitioned Inverse Method for
Parallel Solution of Sparse Triangular Systems",
journal = j-SIAM-J-SCI-COMP,
volume = "15",
number = "1",
pages = "139--148",
month = jan,
year = "1994",
CODEN = "SJOCE3",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Higham:1994:WDM,
author = "Nicholas J. Higham",
title = "Which Dictionary for the Mathematical Scientist?",
journal = j-IMA-BULL,
volume = "30",
number = "5/6",
pages = "81--88",
year = "1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "IMA Bulletin",
}
@TechReport{Braconnier:1995:CFV,
author = "Thierry Braconnier and Nicholas J. Higham",
title = "Computing the Field of Values and Pseudospectra Using
the {Lanczos} Method with Continuation",
type = "Numerical Analysis Report",
number = "279",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "20",
month = nov,
year = "1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Submitted to " # j-BIT,
bibdate = "Fri Jun 10 12:38:34 2011",
acknowledgement = ack-nhfb,
}
@Article{Demmel:1995:SBF,
author = "James W. Demmel and Nicholas J. Higham and Robert S.
Schreiber",
title = "Stability of Block {$ L U $} Factorization",
journal = j-NUM-LIN-ALG-APPL,
volume = "2",
number = "2",
pages = "173--190",
year = "1995",
CODEN = "NLAAEM",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
bibdate = "Wed Apr 5 12:48:23 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear.",
acknowledgement = ack-njh,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
}
@TechReport{Higham:1995:DPS,
author = "Nicholas J. Higham",
title = "Diagonal Pivoting Stability \dots",
type = "Numerical Analysis Report",
number = "2xx",
institution = inst-U-MANCHESTER,
address = inst-U-MANCHESTER:adr,
month = jun,
year = "1995",
bibdate = "Tue Mar 21 16:31:40 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "In preparation.",
acknowledgement = ack-njh,
}
@TechReport{Higham:1995:IRLa,
author = "Nicholas J. Higham",
title = "Iterative Refinement for Linear Systems and {LAPACK}",
type = "Numerical Analysis Report",
number = "277",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "17",
month = sep,
year = "1995",
bibdate = "Mon Apr 21 19:26:38 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in " # j-IMA-J-NUMER-ANAL # " (14) 1997.",
acknowledgement = ack-njh,
mynote = "Also LAPACK Working Note 104.",
}
@TechReport{Higham:1995:IRLb,
author = "N. J. Higham",
title = "Iterative Refinement and {LAPACK}",
type = "LAPACK Working Note",
number = "104",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = oct,
year = "1995",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-95-308, October 1995.",
URL = "http://www.netlib.org/lapack/lawns/lawn104.ps;
http://www.netlib.org/lapack/lawnspdf/lawn104.pdf",
acknowledgement = ack-nhfb,
mynote = "Also Manchester Numerical Analysis Report 277.",
}
@Article{Higham:1995:MPF,
author = "Nicholas J. Higham and Philip A. Knight",
title = "Matrix Powers in Finite Precision Arithmetic",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "16",
number = "2",
pages = "343--358",
month = apr,
year = "1995",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Tue Aug 29 09:11:08 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
mynote = "Page numbers from SIAM.",
}
@Article{Higham:1995:RHA,
author = "Nicholas J. Higham",
title = "Review of {``Howard Anton and Chris Rorres, Elementary
Linear Algebra: Applications Version, Seventh edition,
Wiley, New York, 1994.''}",
journal = j-IMA-BULL,
volume = "31",
number = "7/8",
pages = "122--123",
year = "1995",
bibdate = "Mon Aug 14 03:43:49 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "IMA Bulletin",
}
@TechReport{Higham:1995:SDP,
author = "N. J. Higham",
title = "Stability of the Diagonal Pivoting Method with Partial
Pivoting",
type = "LAPACK Working Note",
number = "105",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = oct,
year = "1995",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-95-309, October 1995.",
URL = "http://www.netlib.org/lapack/lawns/lawn105.ps;
http://www.netlib.org/lapack/lawnspdf/lawn105.pdf",
acknowledgement = ack-nhfb,
}
@Article{Higham:1995:SPT,
author = "Nicholas J. Higham",
title = "Stability of Parallel Triangular System Solvers",
journal = j-SIAM-J-SCI-COMP,
volume = "16",
number = "2",
pages = "400--413",
month = mar,
year = "1995",
CODEN = "SJOCE3",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed Jul 5 10:32:41 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
mynote = "Page numbers from SIAM.",
xxnote = "Check month: apr or mar??",
}
@TechReport{Higham:1995:TMT,
author = "Nicholas J. Higham",
title = "The {Test Matrix Toolbox} for {{\sc Matlab}}, Version
3.0",
type = "Numerical Analysis Report",
number = "276",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "70",
month = sep,
year = "1995",
bibdate = "Thu Sep 28 10:50:20 GMT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/matlab.bib",
note = "Supersedes Numerical Analysis Report No. 237. In
preparation.",
URL = "http://p2chpd-cluster.univ-lyon1.fr/P2CHPD/matlab/pdf_doc/otherdocs/testmatrix.pdf",
acknowledgement = ack-njh,
}
@Article{Braconnier:1996:CFV,
author = "Thierry Braconnier and Nicholas J. Higham",
title = "Computing the Field of Values and Pseudospectra Using
the {Lanczos} Method with Continuation",
journal = j-BIT-NUM-MATH,
volume = "36",
number = "3",
pages = "422--440",
month = sep,
year = "1996",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
MRclass = "65F15",
MRnumber = "97d:65015",
bibdate = "Fri Nov 13 07:00:34 MST 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "International Linear Algebra Year (Toulouse, 1995).",
URL = "http://www.mai.liu.se/BIT/contents/bit36.html",
acknowledgement = ack-njh # " and " # ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Carlisle:1996:LSY,
author = "David P. Carlisle and Nicholas J. Higham",
title = "{\LaTeXe}: {Should} You Upgrade To It?",
journal = j-SIAM-NEWS,
volume = "29",
number = "1",
pages = "12",
month = jan # "\slash " # feb,
year = "1996",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Mon Feb 19 08:51:53 GMT 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@TechReport{Cheng:1996:MCA,
author = "Sheung Hun Cheng and Nicholas J. Higham",
title = "A Modified {Cholesky} Algorithm Based on a Symmetric
Indefinite Factorization",
type = "Numerical Analysis Report",
number = "289",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "18",
month = apr,
year = "1996",
bibdate = "Fri Feb 14 19:47:12 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in " # j-SIAM-J-MAT-ANA-APPL # ".",
acknowledgement = ack-njh,
}
@Article{Hammarling:1996:HPP,
author = "Sven Hammarling and Nicholas J. Higham",
title = "How to Prepare a Poster",
journal = j-SIAM-NEWS,
volume = "29",
number = "4",
pages = "20, 19",
month = may,
year = "1996",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Tue May 14 11:26:42 GMT 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Book{Higham:1996:ASN,
author = "Nicholas J. Higham",
title = "Accuracy and Stability of Numerical Algorithms",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxviii + 688",
year = "1996",
ISBN = "0-89871-355-2 (paperback)",
ISBN-13 = "978-0-89871-355-8 (paperback)",
LCCN = "QA297.H53 1996",
MRclass = "65Fxx, 15-04, 65-02, 65G50",
bibdate = "Tue Jan 30 11:01:35 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
http://www.math.utah.edu/pub/tex/bib/texbook2.bib",
price = "US\$39.00",
URL = "http://www.ma.man.ac.uk/~higham/asna.html",
acknowledgement = ack-njh # " and " # ack-nhfb,
remark = "Typeset with \LaTeX2e.",
tableofcontents = "Principles of Finite Precision Computation \\
Relative Error and Significant Digits \\
Sources of Errors \\
Precision Versus Accuracy \\
Backward and Forward Errors \\
Conditioning \\
Cancellation \\
Solving a Quadratic Equation \\
Computing the Sample Variance \\
Solving Linear Equations \\
Accumulation of Rounding Errors \\
Instability Without Cancellation \\
Increasing the Precision \\
Cancellation of Rounding Errors \\
Rounding Errors Can Be Beneficial \\
Stability of an Algorithm Depends on the Problem \\
Rounding Errors Are Not Random \\
Designing Stable Algorithms \\
Misconceptions \\
Rounding Errors in Numerical Analysis \\
Floating Point Arithmetic \\
Floating Point Number System \\
Model of Arithmetic \\
IEEE Arithmetic \\
Aberrant Arithmetics \\
Exact Subtraction \\
Fused Multiply-Add Operation \\
Choice of Base and Distribution of Numbers \\
Statistical Distribution of Rounding Errors \\
Alternative Number Systems \\
Elementary Functions \\
Accuracy Tests \\
Inner and Outer Products \\
The Purpose of Rounding Error Analysis \\
Running Error Analysis \\
Notation for Error Analysis \\
Matrix Multiplication \\
Complex Arithmetic \\
Miscellany \\
Error Analysis Demystified \\
Other Approaches \\
Summation \\
Summation Methods \\
Error Analysis \\
Compensated Summation \\
Other Summation Methods \\
Statistical Estimates of Accuracy \\
Choice of Method \\
Polynomials \\
Horner's Method \\
Evaluating Derivatives \\
The Newton Form and Polynomial Interpolation \\
Matrix Polynomials \\
Norms \\
Vector Norms",
}
@InCollection{Higham:1996:CCL,
author = "Nicholas J. Higham",
editor = "M. Chu and others",
booktitle = "The {Lanczos} Collected Papers with Commentaries",
title = "{Commentary on C. Lanczos, ``Introduction'' to
``Tables of Chebyshev Polynomials $ S_n(x) $ and $
C_n(x) $'', Nat.\ Bur.\ Stand., Appl.\ Math.\ Series 9,
1952, v--xxvi}",
publisher = "????",
address = "????",
pages = "??--??",
year = "1996",
bibdate = "Fri Jun 10 12:38:34 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "To appear",
acknowledgement = ack-nhfb,
}
@TechReport{Higham:1996:FCS,
author = "Nicholas J. Higham",
title = "Factorizing Complex Symmetric Matrices with Positive
Definite Real and Imaginary Parts",
type = "Numerical Analysis Report",
number = "298",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "12",
month = nov,
year = "1996",
bibdate = "Mon May 19 12:01:10 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Published in \cite{Higham:1998:FCS}.",
acknowledgement = ack-njh,
}
@TechReport{Higham:1996:MIM,
author = "Nicholas J. Higham and Sheung Hun Cheng",
title = "Modifying the Inertia of Matrices Arising in
Optimization",
type = "Numerical Analysis Report",
number = "295",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "17",
month = sep,
year = "1996",
bibdate = "Mon Feb 24 12:42:49 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in " # j-LINEAR-ALGEBRA-APPL # ".",
acknowledgement = ack-njh,
}
@Article{Higham:1996:RAN,
author = "Nicholas J. Higham",
title = "Review of {``Acta Numerica 1994 and Acta Numerica
1995, Cambridge University Press''}",
journal = j-MATH-TODAY,
volume = "32",
number = "1/2",
pages = "28--??",
year = "1996",
ISSN = "1361-2042",
ISSN-L = "1361-2042",
bibdate = "Sat Sep 24 08:44:10 2011",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/Bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
acknowledgement = ack-nhfb # " and " # ack-njh,
fjournal = "Mathematics Today",
journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
}
@Article{Higham:1996:RDB,
author = "Nicholas J. Higham",
title = "Review of {``Dario Bini and Victor Y. Pan. {\em
Polynomial and Matrix Computations. Volume 1:
Fundamental Algorithms}, Birkh{\"a}user, 1994''}",
journal = j-MATH-COMPUT,
volume = "65",
number = "214",
pages = "888--889",
year = "1996",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Wed Jul 17 08:54:13 GMT 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Higham:1996:RMB,
author = "Nicholas J. Higham",
title = "Review of {``Are Magnus Bruaset. A Survey of
Preconditioned Iterative Methods, volume 328 of Pitman
Research Notes in Mathematics. Longman Scientific and
Technical, Essex, UK, 1995.''}",
journal = j-IMA-BULL,
volume = "32",
number = "3/4",
pages = "60",
year = "1996",
bibdate = "Wed Apr 17 16:22:01 GMT 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "IMA Bulletin",
}
@TechReport{Higham:1996:SBE,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "Structured Backward Error and Condition of Generalized
Eigenvalue Problems",
type = "Numerical Analysis Report",
number = "297",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "24",
month = nov,
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Submitted to " # j-SIAM-J-MAT-ANA-APPL,
bibdate = "Fri Nov 15 12:27:07 GMT 1996",
acknowledgement = ack-njh,
}
@TechReport{Cox:1997:ASN,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Accuracy and Stability of the Null Space Method for
Solving the Equality Constrained Least Squares
Problem",
type = "Numerical Analysis Report",
number = "306",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "20",
month = aug,
year = "1997",
bibdate = "Sat Oct 31 10:24:09 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in " # j-BIT # ", 39(1): 1999",
acknowledgement = ack-njh,
}
@TechReport{Cox:1997:SHQ,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Stability of {Householder $ Q R $} Factorization for
Weighted Least Squares Problems",
type = "Numerical Analysis Report",
number = "301",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "17",
month = feb,
year = "1997",
bibdate = "Mon May 19 14:24:46 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in Numerical Analysis 1997, Proceedings of
the 17th Dundee Conference.",
acknowledgement = ack-njh,
}
@InCollection{Higham:1997:CCL,
author = "Nicholas J. Higham",
editor = "William R. Davis and others",
booktitle = "Cornelius Lanczos Collected Published Papers with
Commentaries",
title = "{Commentary on C. Lanczos, ``Introduction'' to
``Tables of Chebyshev Polynomials $ S_n(x) $ and $
C_n(x) $'', Nat.\ Bur.\ Stand., Appl.\ Math.\ Series 9,
1952, v--xxvi}",
volume = "VI(3)",
publisher = "????",
address = "????",
pages = "557--559",
year = "1997",
bibdate = "Wed Aug 13 08:39:47 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear.",
acknowledgement = ack-njh,
mynote = "Volume VI, Part 3, pp. 557--559.",
}
@Article{Higham:1997:IRL,
author = "Nicholas J. Higham",
title = "Iterative refinement for linear systems and {LAPACK}",
journal = j-IMA-J-NUMER-ANAL,
volume = "17",
number = "4",
pages = "495--509",
month = oct,
year = "1997",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/17.4.495",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65F30",
MRnumber = "98e:65036",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www3.oup.co.uk/imanum/hdb/Volume_17/Issue_04/;
MathSciNet database",
note = "Preprint published as Numerical Analysis Report 277,
Manchester Centre for Computational Mathematics,
Manchester, England, and as LAPACK Working Note 104.",
URL = "http://www3.oup.co.uk/imanum/hdb/Volume_17/Issue_04/170495.sgm.abs.html",
abstract = "The technique of iterative refinement for improving
the computed solution to a linear system was used on
desk calculators and computers in the 1940s and has
remained popular. In the 1990s iterative refinement is
well supported in software libraries, notably in
LAPACK. Although the behaviour of iterative refinement
in floating point arithmetic is reasonably well
understood, the existing theory is not sufficient to
justify the use of fixed precision iterative refinement
in all the LAPACK routines in which it is implemented.
We present analysis that provides the theoretical
support needed for LAPACK. The analysis covers both
mixed and fixed precision iterative refinement with an
arbitrary number of iterations, makes only a general
assumption on the underlying solver, and is relatively
short. We identify some remaining open problems.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Higham:1997:MHI,
author = "Nicholas J. Higham",
title = "{Manchester} Hosts Inaugural Meeting of {UK} and
{Irish SIAM Section}",
journal = j-SIAM-NEWS,
volume = "30",
number = "3",
pages = "3",
month = apr,
year = "1997",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@InProceedings{Higham:1997:RDD,
author = "Nicholas J. Higham",
title = "Recent Developments in Dense Numerical Linear
Algebra",
crossref = "Duff:1997:SAN",
pages = "1--26",
year = "1997",
bibdate = "Fri Jul 11 16:11:28 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@Article{Higham:1997:RJR,
author = "Nicholas J. Higham",
title = "Review of {``James R. Schott, Matrix Analysis for
Statistics, Wiley, 1997''}",
journal = j-MATH-TODAY,
volume = "33",
number = "5",
pages = "161--162",
year = "1997",
ISSN = "1361-2042",
ISSN-L = "1361-2042",
bibdate = "Sun Oct 12 15:29:25 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Mathematics Today",
journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
oldlabel = "high97:scho97",
}
@TechReport{Higham:1997:SBF,
author = "Nicholas J. Higham",
title = "Stability of Block $ \mathrm {LDL^T} $ Factorization
of a Symmetric Tridiagonal Matrix",
institution = inst-MCCM,
address = inst-MCCM:adr,
year = "1997",
bibdate = "Wed Aug 20 15:29:39 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "In preparation.",
acknowledgement = ack-njh,
}
@Article{Higham:1997:SDP,
author = "Nicholas J. Higham",
title = "Stability of the Diagonal Pivoting Method with Partial
Pivoting",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "18",
number = "1",
pages = "52--65",
month = jan,
year = "1997",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Sun Mar 2 11:16:54 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@TechReport{Higham:1997:SIMa,
author = "Nicholas J. Higham",
title = "Stable Iterations for the Matrix Square Root",
type = "Numerical Analysis Report",
number = "305",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "20",
month = apr,
year = "1997",
bibdate = "Mon Jun 16 12:13:21 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Published in \cite{Higham:1997:SIMb}.",
acknowledgement = ack-njh,
}
@Article{Higham:1997:SIMb,
author = "Nicholas J. Higham",
title = "Stable iterations for the matrix square root",
journal = j-NUMER-ALGORITHMS,
volume = "15",
number = "2",
pages = "227--242",
month = "????",
year = "1997",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F30 (65F05)",
MRnumber = "98d:65055",
bibdate = "Mon Sep 29 08:36:51 MDT 2003",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
http://www.math.psu.edu/dna/contents/na.html;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/7/6/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/5058/7/6/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@InProceedings{Higham:1997:TLA,
author = "Nicholas J. Higham",
editor = "Ronald F. Boisvert",
booktitle = "Quality of Numerical Software: {Assessment} and
Enhancement",
title = "Testing Linear Algebra Software",
publisher = pub-CH,
address = pub-CH:adr-L,
pages = "109--122",
year = "1997",
bibdate = "Mon Feb 3 09:14:23 GMT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
}
@Article{Cheng:1998:MCA,
author = "Sheung Hun Cheng and Nicholas J. Higham",
title = "A Modified {Cholesky} Algorithm Based on a Symmetric
Indefinite Factorization",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "19",
number = "4",
pages = "1097--1110",
month = oct,
year = "1998",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Dec 4 12:14:09 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/19/4;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/30289",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@TechReport{Cheng:1998:NDP,
author = "Sheung Hun Cheng and Nicholas J. Higham",
title = "The Nearest Definite Pair for the {Hermitian}
Generalized Eigenvalue Problem",
type = "Numerical Analysis Report",
number = "325",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "15",
month = may,
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Submitted to " # j-LINEAR-ALGEBRA-APPL,
bibdate = "Mon May 11 14:55:05 GMT 1998",
acknowledgement = ack-njh,
oldlabel = "chhi98",
}
@TechReport{Cox:1998:BEB,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Backward Error Bounds for Constrained Least Squares
Problems",
type = "Numerical Analysis Report",
number = "321",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "20",
month = apr,
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Submitted to " # j-BIT,
bibdate = "Fri Apr 17 12:13:36 GMT 1998",
acknowledgement = ack-njh,
oldlabel = "cohi98c",
}
@TechReport{Cox:1998:RWB,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Row-Wise Backward Stable Elimination Methods for the
Equality Constrained Least Squares Problem",
type = "Numerical Analysis Report",
number = "319",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "18",
month = mar,
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in " # j-SIAM-J-MAT-ANA-APPL,
bibdate = "Fri Aug 14 18:34:14 GMT 1998",
acknowledgement = ack-njh,
oldlabel = "cohi98r",
}
@InProceedings{Cox:1998:SHQ,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Stability of {Householder QR} Factorization for
Weighted Least Squares Problems",
crossref = "Higham:1998:NAP",
pages = "57--73",
year = "1998",
bibdate = "Mon Aug 29 22:30:58 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
series = "Pitman Research Notes in Mathematics",
acknowledgement = ack-nhfb,
}
@Article{Higham:1998:BNR,
author = "Nicholas J. Higham",
title = "Book News \& Reviews: Review of {``Christoph W.
Ueberhuber, Numerical Computation: Methods, Software
and Analysis, Springer-Verlag, 1997''}",
journal = j-IEEE-COMPUT-SCI-ENG,
volume = "5",
number = "1",
pages = "79--79",
month = jan # "\slash " # mar,
year = "1998",
CODEN = "ISCEE4",
ISSN = "1070-9924 (print), 1558-190X (electronic)",
ISSN-L = "1070-9924",
bibdate = "Sat Jan 9 08:57:23 MST 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://dlib.computer.org/cs/books/cs1998/pdf/c1079.pdf",
acknowledgement = ack-njh # " and " # ack-nhfb,
fjournal = "IEEE Computational Science \& Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=99",
mynote = "Jan-Mar",
oldlabel = "high98:uebe97",
}
@TechReport{Higham:1998:FCP,
author = "Nicholas J. Higham",
title = "{$ Q R $} Factorization with Complete Pivoting and
Accurate Computation of the {SVD}",
type = "Numerical Analysis Report",
number = "324",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "26",
month = sep,
year = "1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Submitted to " # j-LINEAR-ALGEBRA-APPL,
bibdate = "Mon Sep 14 14:06:12 GMT 1998",
acknowledgement = ack-njh,
oldlabel = "high98q",
}
@Article{Higham:1998:FCS,
author = "Nicholas J. Higham",
title = "Factorizing complex symmetric matrices with positive
definite real and imaginary parts",
journal = j-MATH-COMPUT,
volume = "67",
number = "224",
pages = "1591--1599",
year = "1998",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F15 (15A23 65F10 65G05)",
MRnumber = "1 474 652",
bibdate = "Thu Oct 15 16:27:48 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Higham:1998:HWM,
author = "Nicholas J. Higham",
title = "Handbook of Writing for the Mathematical Sciences",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Second",
pages = "xvi + 302",
year = "1998",
ISBN = "0-89871-420-6 (paperback), 0-89871-955-0 (e-book)",
ISBN-13 = "978-0-89871-420-3 (paperback), 978-0-89871-955-0
(e-book)",
LCCN = "QA42 .H54 1998",
bibdate = "Wed Oct 30 14:21:33 2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/texbook3.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Preface to the second edition \\
Preface to the first edition \\
1. General principles \\
2. Writer's tools and recommended reading \\
3. Mathematical writing \\
4. English usage \\
5. When English is a foreign language \\
6. Writing a paper \\
7. Revising a draft \\
8. Publishing a paper \\
9. Writing and defending a thesis \\
10. Writing a talk \\
11. Giving a talk \\
12. Preparing a poster \\
13. TeX and LaTeX \\
14. Aids and resources for writing and research \\
Appendix A. The Greek alphabet \\
Appendix B. Summary of TeX and LaTeX symbols \\
Appendix C. GNU Emacs commands \\
Appendix D. Mathematical and other organizations \\
Appendix E. Prizes for expository writing \\
Glossary \\
Bibliography \\
Name index \\
Subject index",
}
@Article{Higham:1998:MIM,
author = "Nicholas J. Higham and Sheung Hun Cheng",
title = "Modifying the Inertia of Matrices Arising in
Optimization",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "275-276",
pages = "261--279",
year = "1998",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Mon Jul 27 12:37:04 GMT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
oldlabel = "hich98",
}
@TechReport{Higham:1998:NAS,
author = "Nicholas J. Higham",
title = "Notes on Accuracy and Stability of Algorithms in
Numerical Linear Algebra",
type = "Numerical Analysis Report",
number = "333",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "42",
month = aug,
year = "1998",
bibdate = "Mon Sep 7 09:59:00 GMT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "To appear in proceedings of EPSRC Numerical Analysis
Summer School, Leicester University, July 1998.",
acknowledgement = ack-njh,
oldlabel = "high98a",
}
@Article{Higham:1998:NWE,
author = "Nicholas J. Higham and David J. Silvester",
title = "``{Nothing was Ever the Same Again}''",
journal = j-SIAM-NEWS,
volume = "31",
number = "7",
pages = "1, 8",
month = sep,
year = "1998",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Wed Sep 16 11:49:30 GMT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "https://www.siam.org/news/news.php?id=868",
abstract = "In 1948, the world's first stored-program computer
performed its first (dramatic) computation at the
University of Manchester; this spring, researchers
gathered at Manchester to celebrate 50 years of
progress in computers and numerical analysis.",
acknowledgement = ack-njh,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
keywords = "Manchester ``Baby'' computer",
}
@Article{Higham:1998:SBE,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "Structured Backward Error and Condition of Generalized
Eigenvalue Problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "20",
number = "2",
pages = "493--512",
year = "1998",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479896313188",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Dec 4 12:14:09 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/20/2;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/31318",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Cheng:1999:NDP,
author = "Sheung Hun Cheng and Nicholas J. Higham",
title = "The nearest definite pair for the {Hermitian}
generalized eigenvalue problem",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "302-303",
number = "1--3",
pages = "63--76",
day = "1",
month = dec,
year = "1999",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Mon Oct 9 10:54:40 MDT 2000",
bibsource = "http://www.elsevier.com/locate/laa;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/117/25/30/abstract.html;
http://www.elsevier.nl/gej-ng/10/30/19/117/25/30/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Cox:1999:ASN,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Accuracy and Stability of the Null Space Method for
Solving the Equality Constrained Least Squares
Problem",
journal = j-BIT-NUM-MATH,
volume = "39",
number = "1",
pages = "34--49",
month = "????",
year = "1999",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
bibdate = "Thu Oct 16 08:15:34 2003",
bibsource = "http://www.mai.liu.se/BIT/contents/bit39.html;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
OCLC Article1st database",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Cox:1999:BEB,
author = "A. J. Cox and N. J. Higham",
title = "Backward error bounds for constrained least squares
problems",
journal = j-BIT-NUM-MATH,
volume = "39",
number = "2",
pages = "210--227",
month = "????",
year = "1999",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
bibdate = "Thu Oct 16 08:15:34 2003",
bibsource = "http://www.mai.liu.se/BIT/contents/bit39.html;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
OCLC Article1st database",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Higham:1999:BRL,
author = "Nicholas J. Higham",
title = "Book Review: {{\em Linear Algebra (Pure and Applied
Mathematics)}, by Peter D. Lax: 250 pp., \pounds 55.00,
ISBN 0-471-11111-2 (John Wiley \& Sons, 1996)}",
journal = j-BULL-LOND-MATH-SOC,
volume = "31",
number = "3",
pages = "374--375",
month = may,
year = "1999",
CODEN = "LMSBBT",
DOI = "https://doi.org/10.1112/S0024609397264167",
ISSN = "0024-6093 (print), 1469-2120 (electronic)",
ISSN-L = "0024-6093",
bibdate = "Thu Aug 25 10:49:37 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://blms.oxfordjournals.org/content/31/3/374.full.pdf",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the London Mathematical Society",
journal-URL = "http://blms.oxfordjournals.org/content/by/year",
}
@Article{Higham:1999:FBR,
author = "Nicholas J. Higham",
title = "Featured Book Review: {Selected} Books on Numerical
Linear Algebra",
journal = j-SIAM-REVIEW,
volume = "41",
number = "3",
pages = "607--610",
month = sep,
year = "1999",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000041000003000605000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-njh,
created = "1999.05.20",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
updated = "2014.07.26",
}
@Article{Higham:1999:FTP,
author = "Nicholas J. Higham",
title = "A Fitting Tribute to a Pioneering Numerical Analyst
[{Cleve Moler}]",
journal = j-SIAM-NEWS,
volume = "32",
number = "10",
pages = "3",
month = dec,
year = "1999",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib",
note = "Celebrating Cleve Moler's 60th birthday!",
URL = "https://www.siam.org/news/news.php?id=796",
acknowledgement = ack-njh,
created = "2000.01.05",
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
updated = "2000.01.05",
}
@InCollection{Higham:1999:NAS,
author = "Nicholas J. Higham",
title = "Notes on Accuracy and Stability of Algorithms in
Numerical Analysis",
crossref = "Ainsworth:1999:GSG",
pages = "48--82",
year = "1999",
bibdate = "Wed Jul 14 14:57:11 2004",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
}
@Article{Higham:1999:RPD,
author = "Nicholas J. Higham",
title = "Review of {``Peter D. Lax, \booktitle{Linear Algebra},
Wiley, 1997''}",
journal = j-BULL-LOND-MATH-SOC,
volume = "31",
pages = "374--375",
year = "1999",
CODEN = "LMSBBT",
ISSN = "0024-6093 (print), 1469-2120 (electronic)",
ISSN-L = "0024-6093",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
created = "1999.05.27",
fjournal = "Bulletin of the London Mathematical Society",
journal-URL = "http://blms.oxfordjournals.org/content/by/year",
updated = "1999.05.27",
}
@Article{Higham:1999:SBE,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "Structured Backward Error and Condition of Generalized
Eigenvalue Problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "20",
number = "2",
pages = "493--512",
month = apr,
year = "1999",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Dec 4 12:14:09 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/20/2;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/31318",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:1999:SBL,
author = "Nicholas J. Higham",
title = "Stability of block {LDL$^T$} factorization of a
symmetric tridiagonal matrix",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "287",
number = "1--3",
pages = "181--189",
day = "15",
month = jan,
year = "1999",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Fri May 28 08:42:54 MDT 1999",
bibsource = "http://www.elsevier.com/locate/laa;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.elsevier.com/cas/tree/store/laa/sub/1999/287/1-3/6193.pdf;
http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1999&volume=287&issue=1-3&aid=6193",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Cox:2000:RWB,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Row-Wise Backward Stable Elimination Methods for the
Equality Constrained Least Squares Problem",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "21",
number = "1",
pages = "313--326",
month = jan,
year = "2000",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Sat Jan 22 14:39:17 MST 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/21/1;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/33595",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Davies:2000:NSG,
author = "Philip I. Davies and Nicholas J. Higham",
title = "Numerically Stable Generation of Correlation Matrices
and Their Factors",
journal = j-BIT-NUM-MATH,
volume = "40",
number = "4",
pages = "640--651",
month = dec,
year = "2000",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/A:1022384216930",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F18",
MRnumber = "MR1799307 (2002g:65045)",
MRreviewer = "Ram Shanmugam",
bibdate = "Wed Jan 4 15:06:04 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=40&issue=4;
http://www.mai.liu.se/BIT/contents/bit40.html;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=40&issue=4&spage=640",
acknowledgement = ack-nhfb,
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Higham:2000:BAM,
author = "Nicholas J. Higham and Fran{\c{c}}oise Tisseur",
title = "A Block Algorithm for Matrix $1$-Norm Estimation, with
an Application to $1$-Norm Pseudospectra",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "21",
number = "4",
pages = "1185--1201",
month = oct,
year = "2000",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479899356080",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F20 (65F15)",
MRnumber = "MR1780268 (2001d:65051)",
bibdate = "Fri Oct 27 07:23:32 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/21/4;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/35608",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2000:FCP,
author = "Nicholas J. Higham",
title = "{$ Q R $} factorization with complete pivoting and
accurate computation of the {SVD}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "309",
number = "1--3",
pages = "153--174",
year = "2000",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/S0024-3795(99)00230-X",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F20 (15A23)",
MRnumber = "MR1758366 (2001c:65049)",
MRreviewer = "Jesse L. Barlow",
bibdate = "Sat Apr 16 17:54:53 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
remark = "Proceedings of the International Workshop on Accurate
Solution of Eigenvalue Problems (University Park, PA,
1998)",
}
@Book{Higham:2000:MG,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "{MATLAB} Guide",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxii + 283",
year = "2000",
ISBN = "0-89871-469-9",
ISBN-13 = "978-0-89871-469-2",
LCCN = "QA297 .H5217 2000",
MRclass = "65-04 (00A20)",
MRnumber = "MR1787308 (2001e:65003)",
bibdate = "Tue Jan 23 09:04:18 2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
keywords = "Matlab; numerical analysis -- data processing",
}
@Article{Higham:2000:NAQ,
author = "Nicholas J. Higham and Hyun-Min Kim",
title = "Numerical analysis of a quadratic matrix equation",
journal = j-IMA-J-NUMER-ANAL,
volume = "20",
number = "4",
pages = "499--519",
month = oct,
year = "2000",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/20.4.499",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65F30 (15A24)",
MRnumber = "MR1795295 (2001i:65054)",
bibdate = "Mon Feb 12 16:52:03 2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www3.oup.co.uk/imanum/hdb/Volume_20/Issue_04/",
URL = "http://www3.oup.co.uk/imanum/hdb/Volume_20/Issue_04/200499abs.pdf;
http://www3.oup.co.uk/imanum/hdb/Volume_20/Issue_04/pdf/200499.pdf",
abstract = "The quadratic matrix equation $ A X^2 + B X + C = 0 $
in $ n \times n $ matrices arises in applications and
is of intrinsic interest as one of the simplest
nonlinear matrix equations. We give a complete
characterization of solutions in terms of the
generalized Schur decomposition and describe and
compare various numerical solution techniques. In
particular, we give a thorough treatment of functional
iteration methods based on Bernoulli's method. Other
methods considered include Newton's method with exact
line searches, symbolic solution and continued
fractions. We show that functional iteration applied to
the quadratic matrix equation can provide an efficient
way to solve the associated quadratic eigenvalue
problem $ (\lambda^2 A + \lambda B + C) x = 0 $.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Higham:2000:QFC,
author = "Nicholas J. Higham",
title = "{QR} factorization with complete pivoting and accurate
computation of the {SVD}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "309",
number = "1--3",
pages = "153--174",
day = "15",
month = apr,
year = "2000",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Mon Oct 9 10:54:41 MDT 2000",
bibsource = "http://www.elsevier.com/locate/laa;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/126/25/34/abstract.html;
http://www.elsevier.nl/gej-ng/10/30/19/126/25/34/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:2000:RJJ,
author = "Nicholas J. Higham",
title = "Review of {``Jack J. Dongarra, Iain S. Duff, Danny C.
Sorensen, and Henk A. van der Vorst,
\booktitle{Numerical Linear Algebra for
High-Performance Computers}, Society for Industrial and
Applied Mathematics, Philadelphia, PA, USA, 1998''}",
journal = j-SIAM-REVIEW,
volume = "42",
number = "3",
pages = "529",
month = sep,
year = "2000",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000042000003000513000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Oct 6 15:10:21 GMT 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-njh,
created = "2000.10.06",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
updated = "2014.07.26",
}
@TechReport{Anjos:2001:SPA,
author = "M. F. Anjos and N. Higham and M. Takouda and H.
Wolkowicz",
title = "A semidefinite programming approach for the closest
correlation matrix problem",
number = "CORR 2001-in progress",
institution = inst-UNIV-WATERLOO,
address = inst-UNIV-WATERLOO:adr,
year = "2001",
bibdate = "Wed Sep 9 06:36:42 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib",
acknowledgement = ack-nhfb,
}
@Article{Cheng:2001:ALM,
author = "Sheung Hun Cheng and Nicholas J. Higham and Charles S.
Kenney and Alan J. Laub",
title = "Approximating the logarithm of a matrix to specified
accuracy",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "22",
number = "4",
pages = "1112--1125",
year = "2001",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479899364015",
ISSN = "1095-7162",
ISSN-L = "0895-4798",
MRclass = "65F30",
MRnumber = "MR1825853 (2002a:65069)",
MRreviewer = "Jin Yun Yuan",
bibdate = "Sat Apr 16 17:54:57 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@TechReport{Cheng:2001:ILB,
author = "S. Cheng and N. Higham",
title = "Implementation for {LAPACK} of a Block Algorithm for
Matrix $1$-Norm Estimation",
type = "LAPACK Working Note",
number = "152",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = aug,
year = "2001",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "UT-CS-01-470, August 2001.",
URL = "http://www.netlib.org/lapack/lawns/lawn152.ps;
http://www.netlib.org/lapack/lawnspdf/lawn152.pdf",
acknowledgement = ack-nhfb,
}
@Article{Cheng:2001:PIB,
author = "Sheung Hun Cheng and Nicholas J. Higham",
title = "Parallel Implementation of a Block Algorithm for
Matrix $1$-Norm Estimation",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2150",
pages = "568--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:05:53 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2150.htm;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2150/21500568.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2150/21500568.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Davies:2001:ACM,
author = "Philip I. Davies and Nicholas J. Higham and
Fran{\c{c}}oise Tisseur",
title = "Analysis of the {Cholesky} Method with Iterative
Refinement for Solving the Symmetric Definite
Generalized Eigenproblem",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "23",
number = "2",
pages = "472--493",
year = "2001",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479800373498",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15",
MRnumber = "MR1871323 (2002i:65039)",
MRreviewer = "David Scott Watkins",
bibdate = "Fri Feb 22 09:58:16 MST 2002",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/23/2;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/37349",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@TechReport{Higham:2001:BEM,
author = "Nicholas J. Higham and Fran{\c{c}}oise Tisseur",
title = "Bounds for Eigenvalues of Matrix Polynomials",
type = "Numerical Analysis Report",
number = "371",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "16",
month = jan,
year = "2001",
bibdate = "Wed Sep 9 06:38:11 2015",
note = "To appear in " # j-LINEAR-ALGEBRA-APPL,
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib",
acknowledgement = ack-nhfb,
}
@Article{Higham:2001:EPA,
author = "Nicholas J. Higham",
title = "Evaluating {Pad{\'e}} approximants of the matrix
logarithm",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "22",
number = "4",
pages = "1126--1135",
year = "2001",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479800368688",
ISSN = "1095-7162",
ISSN-L = "0895-4798",
MRclass = "65F30 (65D15)",
MRnumber = "MR1824061 (2002d:65039)",
MRreviewer = "Assem Deif",
bibdate = "Sat Apr 16 17:55:00 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2001:P,
author = "Nicholas Higham and Roger Horn and Thomas J. Laffey
and Ferran Puerta",
title = "Preface",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "332--334",
number = "1",
pages = "1--1",
day = "1",
month = aug,
year = "2001",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Jul 25 17:54:46 MDT 2001",
bibsource = "http://www.elsevier.com/locate/laa;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/157/25/25/abstract.html;
http://www.elsevier.nl/gej-ng/10/30/19/157/25/25/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:2001:RMA,
author = "Nicholas J. Higham",
title = "Review of {``Michael Alley, \booktitle{The Craft of
Editing: A Guide for Managers, Scientists and
Engineers}. Springer-Verlag, 2000''}",
journal = j-SIAM-REVIEW,
volume = "43",
number = "1",
pages = "202",
month = mar,
year = "2001",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000043000001000179000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
created = "2001.04.19",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
updated = "2014.07.26",
}
@Article{Higham:2001:SQM,
author = "Nicholas J. Higham and Hyun-Min Kim",
title = "Solving a quadratric matrix equation by {Newton}'s
method with exact line searches",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "23",
number = "2",
pages = "303--316",
year = "2001",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479899350976",
ISSN = "1095-7162",
ISSN-L = "0895-4798",
MRclass = "65H10 (65F30)",
MRnumber = "MR1871314 (2002j:65055)",
bibdate = "Sat Apr 16 17:55:00 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Tisseur:2001:SPP,
author = "Fran{\c{c}}oise Tisseur and Nicholas J. Higham",
title = "Structured pseudospectra for polynomial eigenvalue
problems, with applications",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "23",
number = "1",
pages = "187--208",
year = "2001",
CODEN = "SJMAEL",
ISSN = "1095-7162",
ISSN-L = "0895-4798",
MRclass = "15A18 (15A22 65F15)",
MRnumber = "MR1856605 (2002k:15024)",
MRreviewer = "Jesse L. Barlow",
bibdate = "Sat Apr 16 17:55:00 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Book{Higham:2002:ASN,
author = "Nicholas J. Higham",
title = "Accuracy and Stability of Numerical Algorithms",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Second",
pages = "xxx + 680",
year = "2002",
DOI = "https://doi.org/10.1137/1.9780898718027",
ISBN = "0-89871-521-0 (hardcover), 0-89871-802-3 (e-book)",
ISBN-13 = "978-0-89871-521-7 (hardcover), 978-0-89871-802-7
(e-book)",
LCCN = "QA297 .H53 2002",
MRclass = "65G50 (65-02)",
MRnumber = "MR1927606 (2003g:65064)",
bibdate = "Wed Oct 30 14:20:02 2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
abstract = "\booktitle{Accuracy and Stability of Numerical
Algorithms} gives a thorough, up-to-date treatment of
the behavior of numerical algorithms in finite
precision arithmetic. It combines algorithmic
derivations, perturbation theory, and rounding error
analysis, all enlivened by historical perspective and
informative quotations. This second edition expands and
updates the coverage of the first edition (1996) and
includes numerous improvements to the original
material. Two new chapters treat symmetric indefinite
systems and skew-symmetric systems, and nonlinear
systems and Newton's method. Twelve new sections
include coverage of additional error bounds for
Gaussian elimination, rank revealing $ L U $
factorizations, weighted and constrained least squares
problems, and the fused multiply-add operation found on
some modern computer architectures.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
tableofcontents = "List of Figures \\
List of Tables \\
Preface to Second Edition \\
Preface to First Edition \\
About the Dedication \\
1: Principles of Finite Precision Computation \\
2: Floating Point Arithmetic \\
3: Basics \\
4: Summation \\
5: Polynomials \\
6: Norms \\
7: Perturbation Theory for Linear Systems \\
8: Triangular Systems \\
9: $ L U $ Factorization and Linear Equations \\
10: Cholesky Factorization \\
11: Symmetric Indefinite and Skew-Symmetric Systems \\
12: Iterative Refinement \\
13: Block LU Factorization \\
14: Matrix Inversion \\
15: Condition Number Estimation \\
16: The Sylvester Equation \\
17: Stationary Iterative Methods \\
18: Matrix Powers \\
19: QR Factorization \\
20: The Least Squares Problem \\
21: Underdetermined Systems \\
22: Vandermonde Systems \\
23: Fast Matrix Multiplication \\
24: The Fast Fourier Transform and Applications \\
25: Nonlinear Systems and Newton's Method \\
26: Automatic Error Analysis \\
27: Software Issues in Floating Point Arithmetic \\
28: A Gallery of Test Matrices \\
Appendix A: Solutions to Problems \\
Appendix B: Acquiring Software \\
Appendix C: Program Libraries \\
Appendix D: The Matrix Computation Toolbox \\
Bibliography \\
Name Index \\
Subject Index",
}
@Article{Higham:2002:CNC,
author = "Nicholas J. Higham",
title = "Computing the nearest correlation matrix---a problem
from finance",
journal = j-IMA-J-NUMER-ANAL,
volume = "22",
number = "3",
pages = "329--343",
month = jul,
year = "2002",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/22.3.329",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65F30 (91B02)",
MRnumber = "MR1918653 (2003d:65037)",
bibdate = "Fri Oct 18 09:49:23 MDT 2002",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www3.oup.co.uk/imanum/hdb/Volume_22/Issue_03/",
URL = "http://www3.oup.co.uk/imanum/hdb/Volume_22/Issue_03/220329.sgm.abs.html;
http://www3.oup.co.uk/imanum/hdb/Volume_22/Issue_03/pdf/220329.pdf",
abstract = "Given a symmetric matrix, what is the nearest
correlation matrix that is, the nearest symmetric
positive semidefinite matrix with unit diagonal? This
problem arises in the finance industry, where the
correlations are between stocks. For distance measured
in two weighted Frobenius norms we characterize the
solution using convex analysis. We show how the
modified alternating projections method can be used to
compute the solution for the more commonly used of the
weighted Frobenius norms. In the finance application
the original matrix has many zero or negative
eigenvalues; we show that for a certain class of
weights the nearest correlation matrix has
correspondingly many zero eigenvalues and that this
fact can be exploited in the computation.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "convex analysis; correlation matrix; nearness problem;
positive semidefinite matrix; weighted",
}
@Article{Higham:2002:DDH,
author = "Nicholas J. Higham and Fran{\c{c}}oise Tisseur and
Paul M. {Van Dooren}",
title = "Detecting a definite {Hermitian} pair and a hyperbolic
or elliptic quadratic eigenvalue problem, and
associated nearness problems",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "351--352",
pages = "455--474",
day = "15",
month = aug,
year = "2002",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/S0024-3795(02)00281-1",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "93B60 (15A18 93B40 93C05)",
MRnumber = "MR1917487 (2003f:93047)",
MRreviewer = "A. Barraud",
bibdate = "Fri Aug 9 09:25:01 MDT 2002",
bibsource = "http://www.elsevier.com/locate/laa;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Fourth special issue on linear systems and control",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@TechReport{Higham:2002:MCT,
author = "Nicholas J. Higham",
title = "The {Matrix Computation Toolbox} for {MATLAB} (Version
1.0)",
type = "Numerical Analysis Report",
number = "410",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "19",
month = aug,
year = "2002",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/matlab.bib",
acknowledgement = ack-njh,
created = "2002.08.23",
updated = "2002.08.23",
}
@Article{Higham:2002:MPP,
author = "Nicholas J. Higham and Fran{\c{c}}oise Tisseur",
title = "More on pseudospectra for polynomial eigenvalue
problems and applications in control theory",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "351--352",
pages = "435--453",
day = "15",
month = aug,
year = "2002",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/S0024-3795(01)00542-0",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "93B60 (15A18 65F15)",
MRnumber = "MR1917486 (2003e:93035)",
MRreviewer = "Pablo A. Iglesias",
bibdate = "Fri Aug 9 09:25:01 MDT 2002",
bibsource = "http://www.elsevier.com/locate/laa;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Fourth special issue on linear systems and control",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:2002:RAN,
author = "Nicholas J. Higham",
title = "Review of {``Arnold Neumaier. \booktitle{Introduction
to Numerical Analysis}. Cambridge University Press,
2001''}",
journal = j-SIAM-REVIEW,
volume = "44",
number = "3",
pages = "492--493",
month = sep,
year = "2002",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000044000003000477000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-njh,
created = "2002.09.25",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
updated = "2014.07.26",
}
@Article{Higham:2002:RMO,
author = "Nicholas J. Higham",
title = "Review of {``Michael Overton, \booktitle{Numerical
Computing with IEEE Floating Point Arithmetic:
Including One Theorem, One Rule of Thumb, and One
Hundred and One Exercises}. Society for Industrial and
Applied Mathematics, Philadelphia, PA, USA, 2001''}",
journal = j-SIAM-REVIEW,
volume = "44",
number = "2",
pages = "287--288",
month = jun,
year = "2002",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000044000002000279000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-njh,
created = "2002.07.16",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
updated = "2014.10.13",
}
@Article{Higham:2002:SQM,
author = "Nicholas J. Higham and Hyun-Min Kim",
title = "Solving a Quadratic Matrix Equation by {Newton}'s
Method with Exact Line Searches",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "23",
number = "2",
pages = "303--316",
month = apr,
year = "2002",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Feb 22 09:58:16 MST 2002",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/23/2;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/35097",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Tisseur:2002:SPP,
author = "Fran{\c{c}}oise Tisseur and Nicholas J. Higham",
title = "Structured Pseudospectra for Polynomial Eigenvalue
Problems, with Applications",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "23",
number = "1",
pages = "187--208",
month = jan,
year = "2002",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Wed Oct 23 08:36:32 MDT 2002",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/23/1;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/37145",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Bojanczyk:2003:ECI,
author = "Adam Bojanczyk and Nicholas J. Higham and Harikrishna
Patel",
title = "The equality constrained indefinite least squares
problem: theory and algorithms",
journal = j-BIT,
volume = "43",
number = "3",
pages = "505--517",
year = "2003",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/B:BITN.0000007020.58972.07",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F20",
MRnumber = "MR2026712 (2004m:65049)",
bibdate = "Sat Apr 16 17:55:00 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Bojanczyk:2003:SIL,
author = "Adam Bojanczyk and Nicholas J. Higham and Harikrishna
Patel",
title = "Solving the Indefinite Least Squares Problem by
Hyperbolic {QR} Factorization",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "24",
number = "4",
pages = "914--931",
month = oct,
year = "2003",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479802401497",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F30 (90C20)",
MRnumber = "MR2003312 (2004f:65054)",
MRreviewer = "David Scott Watkins",
bibdate = "Fri Aug 15 05:16:20 MDT 2003",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/24/4;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/40149",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Davies:2003:SPA,
author = "Philip I. Davies and Nicholas J. Higham",
title = "A {Schur--Parlett} Algorithm for Computing Matrix
Functions",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "25",
number = "2",
pages = "464--485",
month = apr,
year = "2003",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479802410815",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F30",
MRnumber = "MR2047429 (2004m:65056)",
bibdate = "Tue Sep 30 10:28:35 MDT 2003",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/25/2;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/41081",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2003:BEM,
author = "Nicholas J. Higham and Fran{\c{c}}oise Tisseur",
title = "Bounds for eigenvalues of matrix polynomials",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "358",
number = "1--3",
pages = "5--22",
day = "1",
month = jan,
year = "2003",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/S0024-3795(01)00316-0",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A42 (15A18 65F15)",
MRnumber = "MR1942721 (2003k:15020)",
MRreviewer = "Ilse C. F. Ipsen",
bibdate = "Mon Apr 28 07:27:21 MDT 2003",
bibsource = "http://www.elsevier.com/locate/laa;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Special issue on accurate solution of eigenvalue
problems (Hagen, 2000)",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/207/25/27/abstract.html;
http://www.sciencedirect.com/science?_ob=GatewayURL&_origin=SOCJLA&_urlversion=4&_method=citationSearch&_version=1&_piikey=S0024379501003160&_volkey=00243795%23358%235&_refkey=Higham%232003%235%2322&md5=51223bc8229cca92374c1fcdbfa6b770",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:2003:CMC,
author = "Nicholas J. Higham and Matthew I. Smith",
title = "Computing the Matrix Cosine",
journal = j-NUMER-ALGORITHMS,
volume = "34",
number = "1",
pages = "13--26",
month = sep,
year = "2003",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1023/A:1026152731904",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F30",
MRnumber = "MR2015575 (2004j:65053)",
bibdate = "Fri Oct 24 09:37:49 MDT 2003",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://ipsapp008.kluweronline.com/content/getfile/5058/47/2/abstract.htm;
http://ipsapp008.kluweronline.com/content/getfile/5058/47/2/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Higham:2003:OMP,
author = "Nicholas J. Higham",
title = "{$J$}-Orthogonal Matrices: Properties and Generation",
journal = j-SIAM-REVIEW,
volume = "45",
number = "3",
pages = "504--519",
month = sep,
year = "2003",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/S0036144502414930",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65F25 (15A23 15A57)",
MRnumber = "MR2046506 (2004m:65054)",
MRreviewer = "Ilse C. F. Ipsen",
bibdate = "Sat Mar 29 09:56:44 MDT 2014",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/45/3;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/41493",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Higham:2003:SPS,
author = "Nicholas J. Higham",
title = "{SIAG/LA} Prizewinners Speed Up the {$ Q R $}
Algorithm",
journal = j-SIAM-NEWS,
volume = "36",
number = "9",
pages = "3",
month = nov,
year = "2003",
ISSN = "0036-1437",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-njh,
created = "1994.01.01",
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
updated = "1994.01.01",
}
@Article{Graham:2004:UAC,
author = "Ivan Graham and Nicholas J. Higham",
title = "{UKIE} Applied\slash Computational Mathematicians
Greet the Year in {Sheffield}, {Manchester}",
journal = j-SIAM-NEWS,
volume = "37",
number = "4",
pages = "12",
month = may,
year = "2004",
ISSN = "0036-1437",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-njh,
created = "1994.01.01",
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
updated = "1994.01.01",
}
@Article{Higham:2004:CPD,
author = "Nicholas J. Higham and D. Steven Mackey and Niloufer
Mackey and Fran{\c{c}}oise Tisseur",
title = "Computing the Polar Decomposition and the Matrix Sign
Decomposition in Matrix Groups",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "25",
number = "4",
pages = "1178--1192",
month = oct,
year = "2004",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479803426644",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A23",
MRnumber = "MR2081137",
bibdate = "Sat Apr 16 10:32:34 MDT 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/25/4;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/42664",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2004:NSB,
author = "Nicholas J. Higham",
title = "The numerical stability of barycentric {Lagrange}
interpolation",
journal = j-IMA-J-NUMER-ANAL,
volume = "24",
number = "4",
pages = "547--556",
month = oct,
year = "2004",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/24.4.547",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65D05",
MRnumber = "MR2094569 (2005e:65007)",
bibdate = "Fri Jul 8 07:42:09 MDT 2005",
bibsource = "http://imanum.oxfordjournals.org/content/vol24/issue4/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://imanum.oupjournals.org/cgi/content/abstract/24/4/547;
http://imanum.oupjournals.org/cgi/reprint/24/4/547",
abstract = "The Lagrange representation of the interpolating
polynomial can be rewritten in two more computationally
attractive forms: a modified Lagrange form and a
barycentric form. We give an error analysis of the
evaluation of the interpolating polynomial using these
two forms. The modified Lagrange formula is shown to be
backward stable. The barycentric formula has a less
favourable error analysis, but is forward stable for
any set of interpolating points with a small Lebesgue
constant. Therefore the barycentric formula can be
significantly less accurate than the modified Lagrange
formula only for a poor choice of interpolating points.
This analysis provides further weight to the argument
of Berrut and Trefethen that barycentric Lagrange
interpolation should be the polynomial interpolation
method of choice.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Bini:2005:AMR,
author = "Dario A. Bini and Nicholas J. Higham and Beatrice
Meini",
title = "Algorithms for the matrix $p$ th root",
journal = j-NUMER-ALGORITHMS,
volume = "39",
number = "4",
pages = "349--378",
month = aug,
year = "2005",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-004-6709-8",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F30",
MRnumber = "MR2134331 (2005m:65094)",
MRreviewer = "Jin Yun Yuan",
bibdate = "Sat May 14 09:10:05 MDT 2005",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=1017-1398;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@InProceedings{Davies:2005:CMF,
author = "Philip I. Davies and Nicholas J. Higham",
editor = "Artan Bori{\c{c}i} and others",
booktitle = "{QCD and numerical analysis III. Proceedings of the
third international workshop on numerical analysis and
lattice QCD, Edinburgh, UK, June 30--July 4, 2003}",
title = "Computing $ f({A})b $ for matrix functions $f$",
volume = "47",
publisher = pub-SPRINGER,
address = pub-SPRINGER:adr-NY,
pages = "15--24",
year = "2005",
DOI = "https://doi.org/10.1007/3-540-28504-0_2",
MRclass = "65F30 (15A99)",
MRnumber = "MR2180116",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
series = "Lecture Notes in Computational Science and
Engineering",
ZMnumber = "1117.65319",
abstract = "For matrix functions $f$ we investigate how to compute
a matrix-vector product $ f(A)b $ without explicitly
computing $ f(A) $. A general method is described that
applies quadrature to the matrix version of the Cauchy
integral theorem. Methods specific to the logarithm,
based on quadrature, and fractional matrix powers,
based on solution of an ordinary differential equation
initial value problem, are also presented.",
acknowledgement = ack-nhfb,
classmath = "65F30 (Other matrix algorithms); 15A54 (Matrices over
function rings)",
keywords = "Cauchy integral theorem; fractional matrix powers;
logarithm; matrix functions; matrix-vector product;
quadrature",
}
@Article{Hargreaves:2005:EAM,
author = "Gareth I. Hargreaves and Nicholas J. Higham",
title = "Efficient algorithms for the matrix cosine and sine",
journal = j-NUMER-ALGORITHMS,
volume = "40",
number = "4",
pages = "383--400",
year = "2005",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-005-8141-0",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F30",
MRnumber = "MR2191973 (2006h:65066)",
bibdate = "Wed May 19 16:29:32 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Higham:2005:BRS,
author = "Nicholas J. Higham",
title = "Book Review: {The SIAM 100-Digit Challenge: A Study in
High-Accuracy Numerical Computing. By Folkmar
Bornemann, Dirk Laurie, Stan Wagon, and J{\"o}rg
Waldvogel. SIAM, Philadelphia, 2004. \$57.00. xii + 306
pp., hardcover. ISBN 0-89871-561-X}",
journal = j-SIAM-REVIEW,
volume = "47",
number = "2",
pages = "382--383",
month = jun,
year = "2005",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri May 27 14:40:10 MDT 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/47/2;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/97149",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Higham:2005:FPM,
author = "Nicholas J. Higham and D. Steven Mackey and Niloufer
Mackey and Fran{\c{c}}oise Tisseur",
title = "Functions Preserving Matrix Groups and Iterations for
the Matrix Square Root",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "26",
number = "3",
pages = "849--877",
month = jul,
year = "2005",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479804442218",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Sat Apr 16 10:32:41 MDT 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/26/3;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/44221",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@TechReport{Higham:2005:IPLa,
author = "Nicholas J. Higham",
title = "An Interview with {Peter Lancaster}",
type = "Numerical Analysis Report",
number = "468",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "10",
month = jun,
year = "2005",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-njh,
created = "2005.06.01",
updated = "2005.06.01",
}
@Article{Higham:2005:IPLb,
author = "Nicholas J. Higham",
title = "An Interview with {Peter Lancaster}",
journal = j-SIAM-NEWS,
volume = "38",
number = "6",
pages = "5--6",
month = jul # "/" # aug,
year = "2005",
ISSN = "0036-1437",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-njh,
created = "2005.08.12",
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
updated = "2005.08.12",
}
@Book{Higham:2005:MG,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "{MATLAB} guide",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Second",
pages = "xxiv + 382",
year = "2005",
ISBN = "0-89871-578-4",
ISBN-13 = "978-0-89871-578-1",
LCCN = "QA297 .H5217 2005",
MRclass = "65-00 (00A20)",
MRnumber = "MR2135945",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
}
@Article{Higham:2005:SSM,
author = "Nicholas J. Higham",
title = "The Scaling and Squaring Method for the Matrix
Exponential Revisited",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "26",
number = "4",
pages = "1179--1193",
month = oct,
year = "2005",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/04061101X",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Thu Dec 29 16:33:50 MST 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/26/4;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/61101",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Guo:2006:SNM,
author = "Chun-Hua Guo and Nicholas J. Higham",
title = "A {Schur--Newton} Method for the Matrix {\boldmath
$p$}th Root and its Inverse",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "28",
number = "3",
pages = "788--804",
month = jan,
year = "2006",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/050643374",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F30",
MRnumber = "MR2262981 (2007k:65071)",
bibdate = "Tue May 18 22:32:12 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2006:CLM,
author = "Nicholas J. Higham and D. Steven Mackey and
Fran{\c{c}}oise Tisseur",
title = "The Conditioning of Linearizations of Matrix
Polynomials",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "28",
number = "4",
pages = "1005--1028",
month = jan,
year = "2006",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/050628283",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (15A18)",
MRnumber = "MR2276551 (2008c:65103)",
MRreviewer = "Marc Van Barel",
bibdate = "Tue May 18 22:32:14 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2006:RAJ,
author = "Nicholas J. Higham",
title = "Review of {``Alan J. Laub. \booktitle{Matrix Analysis
for Scientists and Engineers}''}",
journal = j-SIAM-REVIEW,
volume = "48",
number = "1",
pages = "170--171",
month = mar,
year = "2006",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000048000001000149000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Tue Feb 28 12:58:46 GMT 2006",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-njh,
created = "2006.02.28",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
updated = "2014.07.26",
}
@Article{Higham:2006:RMC,
author = "Nicholas J. Higham",
title = "Review of {``Moody T. Chu and Gene H. Golub.
\booktitle{Inverse Eigenvalue Problems: Theory,
Algorithms, and Applications}''}",
journal = j-J-FLUID-MECH,
volume = "556",
pages = "442--443",
year = "2006",
CODEN = "JFLSA7",
ISSN = "0022-1120 (print), 1469-7645 (electronic)",
ISSN-L = "0022-1120",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
created = "2006.05.11",
fjournal = "Journal of Fluid Mechanics",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=FLM",
updated = "2006.05.11",
}
@Article{Higham:2006:SLM,
author = "Nicholas J. Higham and D. Steven Mackey and Niloufer
Mackey and Fran{\c{c}}oise Tisseur",
title = "Symmetric linearizations for matrix polynomials",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "29",
number = "1",
pages = "143--159",
year = "2006/2007",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/050646202",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (15A18 15A22 93C05)",
MRnumber = "MR2288018 (2008e:65123)",
MRreviewer = "Rafikul Alam",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Corless:2007:SEA,
author = "Robert M. Corless and Hui Ding and Nicholas J. Higham
and David J. Jeffrey",
title = "The solution of $ s \exp (s) = a $ is not always the
{Lambert} $ {W} $ function of $a$",
crossref = "Brown:2007:PIS",
pages = "116--121",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277565",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/issac.bib",
abstract = "We study the solutions of the matrix equation $ S \exp
(S) = A $. Our motivation comes from the study of
systems of delay differential equations $ y'(t) = A y(t
- 1) $, which occur in some models of practical
interest, especially in mathematical biology. This
paper concentrates on the distinction between
evaluating a matrix function and solving a matrix
equation. In particular, it shows that the matrix
Lambert $W$ function evaluated at the matrix $A$ does
not represent all possible solutions of $ S \exp (S) =
A$. These results can easily be extended to more
general matrix equations.",
acknowledgement = ack-nhfb,
keywords = "Lambert $W$ function; matrix function; nonlinear
matrix equation",
}
@Article{Guo:2007:ISN,
author = "Chun-Hua Guo and Nicholas J. Higham",
title = "Iterative Solution of a Nonsymmetric Algebraic
{Riccati} Equation",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "29",
number = "2",
pages = "396--412",
month = "????",
year = "2007",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/050647669",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A24 (15A48 65F30)",
MRnumber = "MR2318355 (2008b:15046)",
MRreviewer = "Ma. Isabel Garc{\'\i}a-Planas",
bibdate = "Tue May 18 22:32:18 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2007:BEP,
author = "Nicholas J. Higham and Ren-Cang Li and Fran{\c{c}}oise
Tisseur",
title = "Backward error of polynomial eigenproblems solved by
linearization",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "29",
number = "4",
pages = "1218--1241",
year = "2007",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/060663738",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (15A18)",
MRnumber = "MR2369292 (2009a:65092)",
MRreviewer = "Jens-Peter M. Zemke",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InCollection{Higham:2007:FM,
author = "Nicholas J. Higham",
title = "Functions of matrices",
crossref = "Hogben:2007:HLA",
pages = "??--??",
year = "2007",
bibdate = "Mon Aug 23 07:45:17 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Higham:2007:MFA,
author = "Nicholas J. Higham",
title = "Matrix Factorizations and Applications: Commentary",
crossref = "Chan:2007:MMC",
pages = "??--??",
year = "2007",
bibdate = "Sat Apr 07 11:25:30 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
}
@Article{Higham:2007:RLT,
author = "Nicholas J. Higham",
title = "Review of {``Lloyd N. Trefethen and Mark Embree.
\booktitle{Spectra and Pseudospectra: The Behavior of
Nonnormal Matrices and Operators}''}",
journal = j-BULL-AMS,
volume = "44",
number = "2",
pages = "277--284",
year = "2007",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
created = "2007.03.21",
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/",
updated = "2007.03.21",
}
@Article{Higham:2007:SLM,
author = "Nicholas J. Higham and D. Steven Mackey and Niloufer
Mackey and Fran{\c{c}}oise Tisseur",
title = "Symmetric Linearizations for Matrix Polynomials",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "29",
number = "1",
pages = "143--159",
month = "????",
year = "2007",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/050646202",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Tue May 18 22:32:16 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Al-Mohy:2008:CFD,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "Computing the {Fr{\'e}chet} derivative of the matrix
exponential, with an application to condition number
estimation",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "30",
number = "4",
pages = "1639--1657",
year = "2008",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/080716426",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F30 (65F35)",
MRnumber = "MR2486857 (2009m:65071)",
MRreviewer = "Dario Fasino",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Guo:2008:DSH,
author = "Chun-Hua Guo and Nicholas J. Higham and
Fran{\c{c}}oise Tisseur",
title = "Detecting and solving hyperbolic quadratic eigenvalue
problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "30",
number = "4",
pages = "1593--1613",
year = "2008",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/070704058",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A18 (15A24 65F30 65H17)",
MRnumber = "MR2486855 (2010b:15021)",
MRreviewer = "Mihai Cipu",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Hale:2008:CRM,
author = "Nicholas Hale and Nicholas J. Higham and Lloyd N.
Trefethen",
title = "Computing {$ {\bf A}^\alpha, \ \log ({\bf A}) $}, and
related matrix functions by contour integrals",
journal = j-SIAM-J-NUMER-ANAL,
volume = "46",
number = "5",
pages = "2505--2523",
year = "2008",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/070700607",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F30",
MRnumber = "MR2421045 (2009e:65071)",
MRreviewer = "Raffaella Pavani",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Higham:2008:BEP,
author = "Nicholas J. Higham and Ren-Cang Li and Fran{\c{c}}oise
Tisseur",
title = "Backward Error of Polynomial Eigenproblems Solved by
Linearization",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "29",
number = "4",
pages = "1218--1241",
month = "????",
year = "2008",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/060663738",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Tue May 18 22:32:22 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2008:CSE,
author = "Nicholas J. Higham",
title = "{Cayley}, {Sylvester}, and early matrix theory",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "428",
number = "1",
pages = "39--43",
year = "2008",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2007.10.004",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15-03 (01A55)",
MRnumber = "MR2372584",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Book{Higham:2008:FMT,
author = "Nicholas J. Higham",
title = "Functions of Matrices: Theory and Computation",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xx + 425",
year = "2008",
DOI = "https://doi.org/10.1137/1.9780898717778",
ISBN = "0-89871-646-2",
ISBN-13 = "978-0-89871-646-7",
MRclass = "15-02 (93B40 93C05)",
MRnumber = "MR2396439 (2009b:15001)",
MRreviewer = "Daniel Kressner",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/numana2000.bib",
note = "Theory and computation",
acknowledgement = ack-nhfb,
}
@Article{Higham:2008:HOW,
author = "Nicholas J. Higham",
title = "In His Own Words [Interview with {Gene Golub}]",
journal = j-SIAM-NEWS,
volume = "41",
number = "1",
pages = "3",
month = jan # "/" # feb,
year = "2008",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Extracts from \cite{high08-ghg}.",
URL = "https://www.siam.org/news/news.php?id=1290",
acknowledgement = ack-njh,
created = "2013.11.28",
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
updated = "2013.11.28",
}
@TechReport{Higham:2008:IGG,
author = "Nicholas J. Higham",
title = "An Interview with {Gene Golub}",
type = "{MIMS EPrint}",
number = "2008.8",
institution = inst-MIMS,
address = inst-MIMS:adr,
pages = "13",
month = feb,
year = "2008",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
created = "2008.02.10",
updated = "2008.02.10",
}
@Misc{Higham:2008:MFT,
author = "Nicholas J. Higham",
title = "The {Matrix Function Toolbox}",
year = "2008",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.maths.manchester.ac.uk/~higham/mftoolbox",
acknowledgement = ack-njh,
created = "2008.01.10",
updated = "2013.12.03",
}
@Article{Higham:2008:SSS,
author = "Nicholas J. Higham and D. Steven Mackey and
Fran{\c{c}}oise Tisseur and Seamus D. Garvey",
title = "Scaling, sensitivity and stability in the numerical
solution of quadratic eigenvalue problems",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "73",
number = "3",
pages = "344--360",
year = "2008",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.2076",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
MRclass = "65N25 (65F15 65H17 74H45 74K05)",
MRnumber = "MR2382048 (2009c:65288)",
MRreviewer = "Gh. Adam",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
}
@Article{Al-Mohy:2009:CFD,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "Computing the {Fr{\'e}chet} Derivative of the Matrix
Exponential, with an Application to Condition Number
Estimation",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "30",
number = "4",
pages = "1639--1657",
month = "????",
year = "2009",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/080716426",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Tue May 18 22:32:31 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Al-Mohy:2009:NSS,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "A new scaling and squaring algorithm for the matrix
exponential",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "3",
pages = "970--989",
year = "2009",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/09074721X",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A16",
MRnumber = "MR2538661",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Guo:2009:DSH,
author = "Chun-Hua Guo and Nicholas J. Higham and
Fran{\c{c}}oise Tisseur",
title = "Detecting and Solving Hyperbolic Quadratic Eigenvalue
Problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "30",
number = "4",
pages = "1593--1613",
month = "????",
year = "2009",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/070704058",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Tue May 18 22:32:31 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Guo:2009:IAA,
author = "Chun-Hua Guo and Nicholas J. Higham and
Fran{\c{c}}oise Tisseur",
title = "An improved arc algorithm for detecting definite
{Hermitian} pairs",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "3",
pages = "1131--1151",
year = "2009",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/08074218X",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A18 (65F18)",
MRnumber = "MR2558816",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2009:CGP,
author = "Nicholas J. Higham and Christian Mehl and
Fran{\c{c}}oise Tisseur",
title = "The canonical generalized polar decomposition",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "4",
pages = "2163--2180",
year = "2009/10",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/090765018",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A23",
MRnumber = "2678962 (2011i:15018)",
MRreviewer = "Marek Niezgoda",
bibdate = "Thu Mar 6 09:16:29 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2009:DMP,
author = "Nicholas J. Higham and D. Steven Mackey and
Fran{\c{c}}oise Tisseur",
title = "Definite Matrix Polynomials and their Linearization by
Definite Pencils",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "2",
pages = "478--502",
month = "????",
year = "2009",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/080721406",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (15A18)",
MRnumber = "MR2530260",
MRreviewer = "Miloud Sadkane",
bibdate = "Tue May 18 22:32:35 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2009:SSM,
author = "Nicholas J. Higham",
title = "The Scaling and Squaring Method for the Matrix
Exponential Revisited",
journal = j-SIAM-REVIEW,
volume = "51",
number = "4",
pages = "747--764",
month = "????",
year = "2009",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/090768539",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65F60 (15A16)",
MRnumber = "MR2563832",
bibdate = "Mon May 17 17:56:49 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/51/4;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Trefethen:2009:DHP,
author = "Anne Trefethen and Nick Higham and Iain Duff and Peter
Coveney",
title = "Developing a High-Performance Computing\slash
Numerical Analysis Roadmap",
journal = j-IJHPCA,
volume = "23",
number = "4",
pages = "423--426",
month = nov,
year = "2009",
CODEN = "IHPCFL",
DOI = "https://doi.org/10.1177/1094342009347710",
ISSN = "1094-3420 (print), 1741-2846 (electronic)",
ISSN-L = "1094-3420",
bibdate = "Tue Aug 31 09:59:45 MDT 2010",
bibsource = "http://hpc.sagepub.com/content/23/4.toc;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://hpc.sagepub.com/content/23/4/423.full.pdf+html",
acknowledgement = ack-nhfb,
journal-URL = "http://hpc.sagepub.com/content/by/year",
}
@Article{Al-Mohy:2010:CSA,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "The complex step approximation to the {Fr{\'e}chet}
derivative of a matrix function",
journal = j-NUMER-ALGORITHMS,
volume = "53",
number = "1",
pages = "133--148",
month = jan,
year = "2010",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-009-9323-y",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F60",
MRnumber = "MR2566131",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=53&issue=1&spage=133",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Al-Mohy:2010:NSS,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "A New Scaling and Squaring Algorithm for the Matrix
Exponential",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "3",
pages = "970--989",
month = "????",
year = "2010",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/09074721X",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Tue May 18 22:32:37 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Borsdorf:2010:CNC,
author = "R{\"u}diger Borsdorf and Nicholas J. Higham and Marcos
Raydan",
title = "Computing a Nearest Correlation Matrix with Factor
Structure",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "5",
pages = "2603--2622",
month = "????",
year = "2010",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/090776718",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F30 (62H25 90C30 90C52)",
MRnumber = "2740623 (2011k:65061)",
MRreviewer = "Anders Linn{\'e}r",
bibdate = "Sun Nov 28 22:55:40 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/31/5;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Borsdorf:2010:PNA,
author = "R{\"u}diger Borsdorf and Nicholas J. Higham",
title = "A preconditioned {Newton} algorithm for the nearest
correlation matrix",
journal = j-IMA-J-NUMER-ANAL,
volume = "30",
number = "1",
pages = "94--107",
month = jan,
year = "2010",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/drn085",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65F20 (62H20 65F25 65H10)",
MRnumber = "MR2580548",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "http://imanum.oxfordjournals.org/content/vol30/issue1/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://imajna.oxfordjournals.org/cgi/content/abstract/30/1/94;
http://imajna.oxfordjournals.org/cgi/reprint/30/1/94",
abstract = "Various methods have been developed for computing the
correlation matrix nearest in the Frobenius norm to a
given matrix. We focus on a quadratically convergent
Newton algorithm recently derived by Qi and Sun.
Various improvements to the efficiency and reliability
of the algorithm are introduced. Several of these
relate to the linear algebra: the Newton equations are
solved by minres instead of the conjugate gradient
method, as it more quickly satisfies the inexact Newton
condition; we apply a Jacobi preconditioner, which can
be computed efficiently even though the coefficient
matrix is not explicitly available; an efficient choice
of eigensolver is identified; and a final scaling step
is introduced to ensure that the returned matrix has
unit diagonal. Potential difficulties caused by
rounding errors in the Armijo line search are avoided
by altering the step selection strategy. These and
other improvements lead to a significant speed-up over
the original algorithm and allow the solution of
problems of dimension a few thousand in a few tens of
minutes.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Guo:2010:IAA,
author = "Chun-Hua Guo and Nicholas J. Higham and
Fran{\c{c}}oise Tisseur",
title = "An Improved Arc Algorithm for Detecting Definite
{Hermitian} Pairs",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "3",
pages = "1131--1151",
month = "????",
year = "2010",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/08074218X",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Tue May 18 22:32:37 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2010:CGP,
author = "Nicholas J. Higham and Christian Mehl and
Fran{\c{c}}oise Tisseur",
title = "The Canonical Generalized Polar Decomposition",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "4",
pages = "2163--2180",
month = "????",
year = "2010",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/090765018",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A23",
MRnumber = "2678962 (2011i:15018)",
MRreviewer = "Marek Niezgoda",
bibdate = "Sun Nov 28 22:55:37 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/31/4;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Higham:2010:CMF,
author = "Nicholas J. Higham and Awad H. Al-Mohy",
title = "Computing matrix functions",
journal = j-ACTA-NUMERICA,
volume = "19",
pages = "159--208",
year = "2010",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S0962492910000036",
ISBN = "0-521-19284-6",
ISBN-13 = "978-0-521-19284-2",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
MRclass = "65F60 (15A16)",
MRnumber = "2652782 (2011g:65073)",
MRreviewer = "Olexander S. Babanin",
bibdate = "Sat Sep 24 10:35:17 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
onlinedate = "10 May 2010",
}
@Article{Al-Mohy:2011:CAM,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "Computing the Action of the Matrix Exponential, with
an Application to Exponential Integrators",
journal = j-SIAM-J-SCI-COMP,
volume = "33",
number = "2",
pages = "488--511",
month = "????",
year = "2011",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/100788860",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F60 (65P10)",
MRnumber = "2785959 (2012d:65082)",
MRreviewer = "Ross A. Lippert",
bibdate = "Fri Mar 4 09:58:54 MST 2011",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/33/2;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/linala2015.bib",
note = "See \cite{Fischer:2017:AAM}.",
URL = "http://epubs.siam.org/sisc/resource/1/sjoce3/v33/i2/p488_s1",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "March 01, 2011",
}
@Article{Grammont:2011:FAN,
author = "Laurence Grammont and Nicholas J. Higham and
Fran{\c{c}}oise Tisseur",
title = "A framework for analyzing nonlinear eigenproblems and
parametrized linear systems",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "435",
number = "3",
pages = "623--640",
day = "1",
month = aug,
year = "2011",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2009.12.038",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A18 (65F15 65F35)",
MRnumber = "2794594 (2012d:15022)",
MRreviewer = "Ilse C. F. Ipsen",
bibdate = "Mon Jun 13 18:34:37 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:2011:RSM,
author = "Nicholas J. Higham and Lijing Lin",
title = "On $p$-th roots of stochastic matrices",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "435",
number = "3",
pages = "448--463",
day = "1",
month = aug,
year = "2011",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2010.04.007",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15B51 (15A16 15B48 60J10)",
MRnumber = "2794585 (2012d:15062)",
MRreviewer = "Adolf Rhodius",
bibdate = "Sat Mar 23 18:05:45 2013",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:2011:SPA,
author = "Nicholas J. Higham and Lijing Lin",
title = "A {Schur--Pad{\'e}} Algorithm for Fractional Powers of
a Matrix",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "32",
number = "3",
pages = "1056--1078",
month = "????",
year = "2011",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/10081232X",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F60",
MRnumber = "2837592",
MRreviewer = "Jorge Sastre",
bibdate = "Thu Feb 9 08:15:43 MST 2012",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/32/3;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "September 29, 2011",
}
@Article{Al-Mohy:2012:IIS,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "Improved Inverse Scaling and Squaring Algorithms for
the Matrix Logarithm",
journal = j-SIAM-J-SCI-COMP,
volume = "34",
number = "4",
pages = "C153--C169",
year = "2012",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/110852553",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F30",
MRnumber = "2970418",
bibdate = "Tue Oct 30 14:49:05 MDT 2012",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/34/4;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2012",
}
@Article{Nakatsukasa:2012:BSI,
author = "Yuji Nakatsukasa and Nicholas J. Higham",
title = "Backward Stability of Iterations for Computing the
Polar Decomposition",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "33",
number = "2",
pages = "460--479",
month = "????",
year = "2012",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/110857544",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F30 (15A23 65F20 65F25 65F35 65G50)",
MRnumber = "2970215",
MRreviewer = "Ilse C. F. Ipsen",
bibdate = "Tue Oct 30 14:04:27 MDT 2012",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/33/2;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2012",
}
@Article{Al-Mohy:2013:CFD,
author = "Awad H. Al-Mohy and Nicholas J. Higham and Samuel D.
Relton",
title = "Computing the {Fr{\'e}chet} derivative of the matrix
logarithm and estimating the condition number",
journal = j-SIAM-J-SCI-COMP,
volume = "35",
number = "4",
pages = "C394--C410",
year = "2013",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/120885991",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F60 (65F35)",
MRnumber = "3080997",
bibdate = "Thu Mar 6 09:16:29 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Betcke:2013:NCN,
author = "Timo Betcke and Nicholas J. Higham and Volker Mehrmann
and Christian Schr{\"o}der and Fran{\c{c}}oise
Tisseur",
title = "{NLEVP}: a collection of nonlinear eigenvalue
problems",
journal = j-TOMS,
volume = "39",
number = "2",
pages = "Art. 7, 28",
year = "2013",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2427023.2427024",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65H17 (65F10 65Y15)",
MRnumber = "3031626",
bibdate = "Thu Mar 6 09:16:29 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Dingle:2013:RIT,
author = "Nicholas J. Dingle and Nicholas J. Higham",
title = "Reducing the influence of tiny normwise relative
errors on performance profiles",
journal = j-TOMS,
volume = "39",
number = "4",
pages = "24:1--24:11",
month = jul,
year = "2013",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2491491.2491494",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65F35 (65G50 65Y20)",
MRnumber = "3092099",
MRreviewer = "Dario Fasino",
bibdate = "Fri Jul 19 17:20:56 MDT 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "It is a widespread but little-noticed phenomenon that
the normwise relative error $ || x - y || / || x || $
of vectors $x$ and $y$ of floating point numbers of the
same precision, where $y$ is an approximation to x, can
be many orders of magnitude smaller than the unit
roundoff. We analyze this phenomenon and show that in
the $ \infty $-norm it happens precisely when $x$ has
components of widely varying magnitude and every
component of $x$ of largest magnitude agrees with the
corresponding component of $y$. Performance profiles
are a popular way to compare competing algorithms
according to particular measures of performance. We
show that performance profiles based on normwise
relative errors can give a misleading impression due to
the influence of zero or tiny normwise relative errors.
We propose a transformation that reduces the influence
of these extreme errors in a controlled manner, while
preserving the monotonicity of the underlying data and
leaving the performance profile unchanged at its left
end-point. Numerical examples with both artificial and
genuine data illustrate the benefits of the
transformation.",
acknowledgement = ack-nhfb,
articleno = "24",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Higham:2013:ISP,
author = "Nicholas J. Higham and Lijing Lin",
title = "An improved {Schur--Pad{\'e}} algorithm for fractional
powers of a matrix and their {Fr{\'e}chet}
derivatives",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "34",
number = "3",
pages = "1341--1360",
month = "????",
year = "2013",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/130906118",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F60 (15A16)",
MRnumber = "3102571",
bibdate = "Tue Feb 11 12:44:41 MST 2014",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/34/3;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2013",
}
@Article{Nakatsukasa:2013:SES,
author = "Yuji Nakatsukasa and Nicholas J. Higham",
title = "Stable and Efficient Spectral Divide and Conquer
Algorithms for the Symmetric Eigenvalue Decomposition
and the {SVD}",
journal = j-SIAM-J-SCI-COMP,
volume = "35",
number = "3",
pages = "A1325--A1349",
month = "????",
year = "2013",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/120876605",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15",
MRnumber = "3054594",
MRreviewer = "Fatemeh Panjeh Ali Beik",
bibdate = "Fri Jul 19 07:43:53 MDT 2013",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/35/3;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
note = "See \cite{Sukkari:2019:QBS}.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2013",
}
@Article{Aprahamian:2014:MUF,
author = "Mary Aprahamian and Nicholas J. Higham",
title = "The matrix unwinding function, with an application to
computing the matrix exponential",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "35",
number = "1",
pages = "88--109",
month = "????",
year = "2014",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/130920137",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F30 (15A24 65F60)",
MRnumber = "3159979",
MRreviewer = "Petko Petkov",
bibdate = "Mon Mar 31 06:45:43 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2014",
}
@Article{Bethune:2014:PAA,
author = "Iain Bethune and J. Mark Bull and Nicholas J. Dingle
and Nicholas J. Higham",
title = "Performance analysis of asynchronous {Jacobi}'s method
implemented in {MPI}, {SHMEM} and {OpenMP}",
journal = j-IJHPCA,
volume = "28",
number = "1",
pages = "97--111",
month = feb,
year = "2014",
CODEN = "IHPCFL",
DOI = "https://doi.org/10.1177/1094342013493123",
ISSN = "1094-3420 (print), 1741-2846 (electronic)",
ISSN-L = "1094-3420",
bibdate = "Fri Mar 14 15:39:59 MDT 2014",
bibsource = "http://hpc.sagepub.com/content/28/1.toc;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/ijsa.bib;
http://www.math.utah.edu/pub/tex/bib/pvm.bib",
URL = "http://hpc.sagepub.com/content/28/1/97.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "International Journal of High Performance Computing
Applications",
journal-URL = "http://hpc.sagepub.com/content/by/year",
onlinedate = "July 11, 2013",
}
@Article{Higham:2014:ECN,
author = "Nicholas J. Higham and Samuel D. Relton",
title = "Estimating the condition number of the {Fr{\'e}chet}
derivative of a matrix function",
journal = j-SIAM-J-SCI-COMP,
volume = "36",
number = "6",
pages = "C617--C634",
year = "2014",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/130950082",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F35 (65F60)",
MRnumber = "3281285",
MRreviewer = "A. Bultheel",
bibdate = "Wed Sep 9 06:09:29 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
ZMnumber = "06409885",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Higham:2014:HOF,
author = "Nicholas J. Higham and Samuel D. Relton",
title = "Higher Order {Fr{\'e}chet} Derivatives of Matrix
Functions and the Level-$2$ Condition Number",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "35",
number = "3",
pages = "1019--1037",
month = "????",
year = "2014",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/130945259",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F35 (15A16 65F60)",
MRnumber = "3233937",
MRreviewer = "Boyan G. Zlatanov",
bibdate = "Sat Sep 13 12:06:59 MDT 2014",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/35/3;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2014",
}
@Article{Higham:2014:SIA,
author = "Nicholas J. Higham",
title = "{Sylvester}'s influence on applied mathematics",
journal = j-MATH-TODAY,
volume = "50",
number = "4",
pages = "202--206",
year = "2014",
ISSN = "1361-2042",
ISSN-L = "1361-2042",
MRclass = "01A70",
MRnumber = "3241571",
bibdate = "Wed Sep 9 06:09:29 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Today",
journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
}
@Article{Lin:2014:CSR,
author = "Lijing Lin and Nicholas J. Higham and Jianxin Pan",
title = "Covariance structure regularization via entropy loss
function",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "72",
pages = "315--327",
year = "2014",
CODEN = "CSDADW",
DOI = "https://doi.org/10.1016/j.csda.2013.10.004",
ISSN = "0167-9473 (print), 1872-7352 (electronic)",
ISSN-L = "0167-9473",
MRclass = "Preliminary Data",
MRnumber = "3139365",
bibdate = "Thu Mar 6 09:16:29 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/01679473",
}
@Article{Al-Mohy:2015:NAC,
author = "Awad H. Al-Mohy and Nicholas J. Higham and Samuel D.
Relton",
title = "New algorithms for computing the matrix sine and
cosine separately or simultaneously",
journal = j-SIAM-J-SCI-COMP,
volume = "37",
number = "1",
pages = "A456--A487",
year = "2015",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/140973979",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F60",
MRnumber = "3311875",
MRreviewer = "Petko Petkov",
bibdate = "Wed Sep 9 06:09:29 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
ZMnumber = "1315.65045",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Fasi:2015:AML,
author = "Massimiliano Fasi and Nicholas J. Higham and Bruno
Iannazzo",
title = "An algorithm for the matrix {Lambert} {$W$} function",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "36",
number = "2",
pages = "669--685",
month = "????",
year = "2015",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/140997610",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F60 (15A15)",
MRnumber = "3354997",
MRreviewer = "Thomas Mach",
bibdate = "Fri Aug 7 16:43:51 MDT 2015",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/36/2;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
ZMnumber = "1317.65116",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2015",
}
@Misc{Higham:2015:MCT,
author = "Nicholas J. Higham",
title = "Matrix Computation Toolbox",
howpublished = "Web site.",
year = "2015",
bibdate = "Sat Apr 01 08:14:19 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/matlab.bib",
URL = "http://www.ma.man.ac.uk/~higham/mctoolbox",
abstract = "The Matrix Computation Toolbox is a collection of
MATLAB M-files containing functions for constructing
test matrices, computing matrix factorizations,
visualizing matrices, and carrying out direct search
optimization. Various other miscellaneous functions are
also included. This toolbox supersedes the author's
earlier Test Matrix Toolbox (final release
1995).\par
The toolbox was developed in conjunction with the book
Accuracy and Stability of Numerical Algorithms (SIAM,
Second edition, August 2002, xxx + 680 pp.). That book
is the primary documentation for the toolbox: it
describes much of the underlying mathematics and many
of the algorithms and matrices (it also describes many
of the matrices provided by MATLAB's gallery
function).",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; MATLAB",
}
@InCollection{Higham:2015:MFS,
author = "Nicholas J. Higham and Lijing Lin",
editor = "Zhaojun Bai and Weiguo Gao and Yangfeng Su",
booktitle = "Matrix Functions and Matrix Equations",
title = "Matrix Functions: a Short Course",
volume = "19",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
bookpages = "vii + 137",
pages = "1--27",
year = "2015",
ISBN = "981-4675-76-8 (hardcover), 981-4675-77-6 (e-book),
981-4675-78-4 (e-book)",
ISBN-13 = "978-981-4675-76-5 (hardcover), 978-981-4675-77-2
(e-book), 978-981-4675-78-9 (e-book)",
LCCN = "QA184.2 .M39 2015",
MRclass = "15-01",
MRnumber = "3445562",
bibdate = "Sat Aug 26 17:36:15 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
series = "Ser. Contemp. Appl. Math. CAM",
URL = "http://www.worldscientific.com/worldscibooks/10.1142/9590",
acknowledgement = ack-nhfb,
tableofcontents = "Matrix Functions: A Short Course / Nicholas J.
Higham and Lijing Lin / 1 \\
A Short Course on Exponential Integrators / Marlis
Hochbruck / 28 \\
Matrix Equations and Model Reduction / Peter Benner,
Tobias Breiten and Lihong Feng / 50 \\
Rayleigh Quotient Based Optimization Methods for
Eigenvalue Problems / Ren-Cang Li / 76 \\
Factorization-Based Sparse Solvers and Preconditioners
/ Xiaoye Sherry Li / 109",
xxaddress = "Beijing, China",
xxpublisher = "Higher Education Press",
}
@Article{Aprahamian:2016:MEB,
author = "Mary Aprahamian and Desmond J. Higham and Nicholas J.
Higham",
title = "Matching exponential-based and resolvent-based
centrality measures",
journal = j-J-COMPLEX-NETWORKS,
volume = "4",
number = "2",
pages = "157--176",
year = "2016",
DOI = "https://doi.org/10.1093/comnet/cnv016",
ISSN = "2051-1310 (print), 2051-1329 (electronic)",
ISSN-L = "2051-1310",
MRclass = "05C82",
MRnumber = "3605538",
bibdate = "Sat Aug 26 17:36:42 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Complex Netw.",
fjournal = "Journal of Complex Networks",
journal-URL = "http://www.comnet.oxfordjournals.org",
}
@Article{Aprahamian:2016:MIT,
author = "Mary Aprahamian and Nicholas J. Higham",
title = "Matrix Inverse Trigonometric and Inverse Hyperbolic
Functions: Theory and Algorithms",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "37",
number = "4",
pages = "1453--1477",
month = "????",
year = "2016",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/16M1057577",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A24 (65F60)",
MRnumber = "3556068",
MRreviewer = "Mustapha Rachidi",
bibdate = "Fri Aug 25 09:01:43 MDT 2017",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/37/4;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2016",
}
@Article{Deadman:2016:TMF,
author = "Edvin Deadman and Nicholas J. Higham",
title = "Testing Matrix Function Algorithms Using Identities",
journal = j-TOMS,
volume = "42",
number = "1",
pages = "4:1--4:15",
month = feb,
year = "2016",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2723157",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65F60",
MRnumber = "3472420",
bibdate = "Tue Mar 1 17:07:56 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Algorithms for computing matrix functions are
typically tested by comparing the forward error with
the product of the condition number and the unit
roundoff. The forward error is computed with the aid of
a reference solution, typically computed at high
precision. An alternative approach is to use functional
identities such as the ``round-trip tests'' $ e^{\log
A} = A $ and $ (A^{1 / p})^p = A $, as are currently
employed in a SciPy test module. We show how a
linearized perturbation analysis for a functional
identity allows the determination of a maximum residual
consistent with backward stability of the constituent
matrix function evaluations. Comparison of this maximum
residual with a computed residual provides a necessary
test for backward stability. We also show how the
actual linearized backward error for these relations
can be computed. Our approach makes use of Fr{\'e}chet
derivatives and estimates of their norms. Numerical
experiments show that the proposed approaches are able
both to detect instability and to confirm stability.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Higham:2016:AAA,
author = "Nicholas J. Higham and Nata{\v{s}}a Strabi{\'c}",
title = "{Anderson} acceleration of the alternating projections
method for computing the nearest correlation matrix",
journal = j-NUMER-ALGORITHMS,
volume = "72",
number = "4",
pages = "1021--1042",
month = aug,
year = "2016",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-015-0078-3",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F30 (15B57)",
MRnumber = "3529831",
MRreviewer = "Hassane Abbas",
bibdate = "Tue Sep 20 10:57:47 MDT 2016",
bibsource = "http://link.springer.com/journal/11075/72/4;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://link.springer.com/content/pdf/10.1007/s11075-015-0078-3.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Higham:2016:ACP,
author = "Nicholas J. Higham and Vanni Noferini",
title = "An algorithm to compute the polar decomposition of a $
3 \times 3 $ matrix",
journal = j-NUMER-ALGORITHMS,
volume = "73",
number = "2",
pages = "349--369",
month = oct,
year = "2016",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-016-0098-7",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F99 (15A21)",
MRnumber = "3549082",
bibdate = "Tue Sep 20 10:57:48 MDT 2016",
bibsource = "http://link.springer.com/journal/11075/73/2;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://link.springer.com/content/pdf/10.1007/s11075-016-0098-7.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "$3 \times 3$ matrix; Numerical stability; Polar
decomposition; Quaternions; Singular value
decomposition",
}
@Article{Higham:2016:BDN,
author = "Nicholas J. Higham and Natasa Strabi{\'c}",
title = "Bounds for the Distance to the Nearest Correlation
Matrix",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "37",
number = "3",
pages = "1088--1102",
month = "????",
year = "2016",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/15M1052007",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A45 (65F05 65F30)",
MRnumber = "3537883",
MRreviewer = "Antonio Cicone",
bibdate = "Tue Nov 8 08:41:57 MST 2016",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/37/3;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2016",
}
@Article{Higham:2016:ELE,
author = "Nicholas J. Higham and Samuel D. Relton",
title = "Estimating the Largest Elements of a Matrix",
journal = j-SIAM-J-SCI-COMP,
volume = "38",
number = "5",
pages = "C584--C601",
month = "????",
year = "2016",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/15M1053645",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F99 (65F35)",
MRnumber = "3561776",
MRreviewer = "Jo\~ao Ribeiro Cardoso",
bibdate = "Sun Mar 12 07:28:39 MDT 2017",
bibsource = "http://epubs.siam.org/toc/sjoce3/38/5;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2016",
}
@Article{Higham:2016:KGS,
author = "Nicholas J. Higham",
title = "{Knuth} Gives Satisfaction in {SIAM von Neumann
Lecture}",
journal = j-SIAM-NEWS,
volume = "49",
number = "6",
pages = "??--??",
month = jul # "\slash " # aug,
year = "2016",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Fri Sep 30 15:20:42 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "https://sinews.siam.org/DetailsPage/TabId/900/ArtMID/2243/ArticleID/820/Knuth-Gives-Satisfaction-in-SIAM-von-Neumann-Lecture.aspx",
acknowledgement = ack-nhfb,
keywords = "2016 SIAM John von Neumann lecture prize; Art of
Computer Programming; Donald E. Knuth; Satisfiability
and Combinatorics",
}
@Article{Higham:2016:MWP,
author = "Nicholas J. Higham",
title = "Mathematical Word Processing: Historical Snippets",
journal = j-SIAM-NEWS,
volume = "49",
number = "6",
pages = "??--??",
month = jul # "\slash " # aug,
year = "2016",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Fri Sep 30 12:32:57 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "https://sinews.siam.org/DetailsPage/TabId/900/ArtMID/2243/ArticleID/1655/Mathematical-Word-Processing-Historical-Snippets.aspx",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Article{Higham:2016:RDS,
author = "Nicholas J. Higham and Nata{\v{s}}a Strabi{\'c} and
Vedran {\v{S}}ego",
title = "Restoring Definiteness via Shrinking, with an
Application to Correlation Matrices with a Fixed
Block",
journal = j-SIAM-REVIEW,
volume = "58",
number = "2",
pages = "245--263",
month = "????",
year = "2016",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/140996112",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "15B57 (65F30)",
MRnumber = "3493945",
MRreviewer = "Yang Cao",
bibdate = "Fri May 27 07:15:57 MDT 2016",
bibsource = "http://epubs.siam.org/toc/siread/58/2;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 2016",
}
@Article{Carson:2017:NAI,
author = "Erin Carson and Nicholas J. Higham",
title = "A new analysis of iterative refinement and its
application to accurate solution of ill-conditioned
sparse linear systems",
journal = j-SIAM-J-SCI-COMP,
volume = "39",
number = "6",
pages = "A2834--A2856",
year = "2017",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/17M1122918",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65G50 (65F10 65F35 65F50)",
MRnumber = "3732948",
bibdate = "Tue May 8 08:38:21 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "http://eprints.maths.manchester.ac.uk/2537/",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Fischer:2017:AAM,
author = "Thomas M. Fischer",
title = "On the algorithm by {Al-Mohy} and {Higham} for
computing the action of the matrix exponential: a
posteriori roundoff error estimation",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "531",
number = "??",
pages = "141--168",
day = "15",
month = oct,
year = "2017",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2017.05.042",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Sat Aug 26 17:24:35 MDT 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/linala2015.bib",
note = "See \cite{Al-Mohy:2011:CAM}.",
URL = "http://www.sciencedirect.com/science/article/pii/S0024379517303427",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:2017:CAT,
author = "Nicholas J. Higham and Peter Kandolf",
title = "Computing the Action of Trigonometric and Hyperbolic
Matrix Functions",
journal = j-SIAM-J-SCI-COMP,
volume = "39",
number = "2",
pages = "A613--A627",
month = "????",
year = "2017",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/16M1084225",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F60 (15A16)",
MRnumber = "3636536",
MRreviewer = "Ralf Zimmermann",
bibdate = "Fri Aug 25 09:17:35 MDT 2017",
bibsource = "http://epubs.siam.org/toc/sjoce3/39/2;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2017",
}
@Article{Higham:2017:CHB,
author = "Nicholas J. Higham and Neville J. Ford",
title = "{Christopher T. H. Baker} (1939--2017)",
journal = j-MATH-TODAY,
volume = "53",
number = "6",
pages = "257",
year = "2017",
ISSN = "1361-2042",
ISSN-L = "1361-2042",
MRclass = "01A70",
MRnumber = "3702305",
bibdate = "Tue May 8 08:39:11 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Today",
journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
}
@Book{Higham:2017:MG,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "{MATLAB} guide",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxvi + 476",
year = "2017",
ISBN = "1-61197-465-8",
ISBN-13 = "978-1-61197-465-2",
MRclass = "65-00 (00A20)",
MRnumber = "3601107",
bibdate = "Sat Aug 26 17:40:10 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/matlab.bib;
http://www.math.utah.edu/pub/tex/bib/numana2010.bib",
abstract = "MATLAB is an interactive system for numerical
computation that is widely used for teaching and
research in industry and academia. It provides a modern
programming language and problem solving environment,
with powerful data structures, customizable graphics,
and easy-to-use editing and debugging tools. This third
edition of MATLAB Guide completely revises and updates
the best-selling second edition and is more than 25
percent longer. The book remains a lively, concise
introduction to the most popular and important features
of MATLAB and the Symbolic Math Toolbox. Key features
are a tutorial in Chapter 1 that gives a hands-on
overview of MATLAB, a thorough treatment of MATLAB
mathematics, including the linear algebra and numerical
analysis functions and the differential equation
solvers, and a web page that provides a link to example
program files, updates, and links to MATLAB resources.
The new edition contains color figures throughout,
includes pithy discussions of related topics in new
`Asides' boxes that augment the text, has new chapters
on the Parallel Computing Toolbox, object-oriented
programming, graphs, and large data sets, covers
important new MATLAB data types such as categorical
arrays, string arrays, tall arrays, tables, and
timetables, contains more on MATLAB workflow, including
the Live Editor and unit tests, and fully reflects
major updates to the MATLAB graphics system.",
acknowledgement = ack-nhfb,
remark = "Third edition of
\cite{Higham:2000:MG,Higham:2005:MG}.",
subject = "MATLAB (logiciel).; Analyse num{\'e}rique; Logiciels.;
Numerical analysis; Data processing; Data processing.",
tableofcontents = "1: A Brief Tutorial \\
2: Basics \\
3: Distinctive Features of MATLAB \\
4: Arithmetic \\
5: Matrices \\
6: Operators and Flow Control \\
7: Program Files \\
8: Graphics \\
9: Linear Algebra \\
10: More on Functions \\
11: Numerical Methods: Part I \\
12: Numerical Methods: Part II \\
13: Input and Output \\
14: Troubleshooting \\
15: Sparse Matrices \\
16: More on Coding \\
17: Advanced Graphics \\
18: Other Data Types and Multidimensional Arrays \\
19: Object-Oriented Programming \\
20: The Symbolic Math Toolbox \\
21: Graphs \\
22: Large Data Sets \\
23: Optimizing Codes \\
24: Tricks and Tips \\
25: The Parallel Computing Toolbox \\
26: Case Studies",
}
@InProceedings{Higham:2017:RMA,
author = "N. J. Higham",
title = "The Rise of Multiprecision Arithmetic",
crossref = "Burgess:2017:ISC",
pages = "1--1",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.24",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "There is a growing demand for and availability of
multiprecision arithmetic: floating point arithmetic
supporting multiple, possibly arbitrary, precisions.
For an increasing body of applications, including in
supernova simulations, electromagnetic scattering
theory, and computational number theory, double
precision arithmetic is insufficient to provide results
of the required accuracy. On the other hand, for
climate modelling and deep learning half precision
(about four significant decimal digits) has been shown
to be sufficient in some studies. We discuss a number
of topics involving multiprecision arithmetic,
including: The need for, availability of, and ways to
exploit, higher precision arithmetic (e.g., quadruple
precision arithmetic). How to derive linear algebra
algorithms that will run in any precision, as opposed
to be being optimized (as some key algorithms are) for
double precision. For solving linear systems with the
use of iterative refinement, the benefits of suitably
combining three different precisions of arithmetic
(say, half, single, and double). How a new form of
preconditioned iterative refinement can be used to
solve very ill conditioned sparse linear systems to
high accuracy.",
acknowledgement = ack-nhfb,
keywords = "climate modelling; Computational modeling; deep
learning half precision; Digital arithmetic; double
precision arithmetic; Electromagnetic scattering;
floating point arithmetic; Floating-point arithmetic;
iterative methods; iterative refinement; linear
algebra; linear algebra algorithms; linear systems;
Linear systems; Mathematical model; multiprecision
arithmetic; sparse linear systems",
}
@Article{Carson:2018:ASL,
author = "Erin Carson and Nicholas J. Higham",
title = "Accelerating the Solution of Linear Systems by
Iterative Refinement in Three Precisions",
journal = j-SIAM-J-SCI-COMP,
volume = "40",
number = "2",
pages = "A817--A847",
month = "????",
year = "2018",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/17M1140819",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F10 (65F05 65F35 65G50)",
MRnumber = "3775138",
MRreviewer = "Dimitrios Christou",
bibdate = "Tue May 8 15:57:34 MDT 2018",
bibsource = "http://epubs.siam.org/toc/sjoce3/40/2;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2018",
}
@Article{Fasi:2018:MAC,
author = "Massimiliano Fasi and Nicholas J. Higham",
title = "Multiprecision algorithms for computing the matrix
logarithm",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "39",
number = "1",
pages = "472--491",
year = "2018",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/17M1129866",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F60 (15A16 15A60)",
MRnumber = "3775134",
MRreviewer = "Javier Pastor",
bibdate = "Tue May 8 08:39:52 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Freeman:2018:JWF,
author = "T. L. Freeman and Nicholas J. Higham",
title = "{Joan E. Walsh FIMA} (1932--2017)",
journal = j-MATH-TODAY,
volume = "54",
number = "3",
pages = "89",
year = "2018",
ISSN = "1361-2042",
ISSN-L = "1361-2042",
MRclass = "01A70",
MRnumber = "3820884",
bibdate = "Sat Oct 6 15:34:30 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Today",
journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
}
@Article{Georgescu:2018:ESC,
author = "Dan I. Georgescu and Nicholas J. Higham and Gareth W.
Peters",
title = "Explicit solutions to correlation matrix completion
problems, with an application to risk management and
insurance",
journal = j-R-SOC-OPEN-SCI,
volume = "5",
number = "3",
pages = "172348:1--172348:11",
month = mar,
year = "2018",
CODEN = "RSOSAV",
DOI = "https://doi.org/10.1098/rsos.172348",
ISSN = "2054-5703",
ISSN-L = "2054-5703",
MRclass = "65F99 (15A83 91B30)",
MRnumber = "3815440",
bibdate = "Sat Oct 6 15:34:30 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
ajournal = "R. Soc. Open Sci.",
fjournal = "Royal Society Open Science",
journal-URL = "http://rsos.royalsocietypublishing.org/",
}
@InProceedings{Haidar:2018:HGT,
author = "Azzam Haidar and Stanimire Tomov and Jack Dongarra and
Nicholas J. Higham",
editor = "{IEEE}",
booktitle = "{SC '18 Proceedings of the International Conference
for High Performance Computing, Networking, Storage,
and Analysis, Dallas, Texas, November 11--16, 2018}",
title = "Harnessing {GPU} tensor cores for fast {FP16}
arithmetic to speed up mixed-precision iterative
refinement solvers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "47:1--47:11",
year = "2018",
ISBN = "1-5386-8384-9",
ISBN-13 = "978-1-5386-8384-2",
LCCN = "????",
bibdate = "Sat Jan 19 18:51:19 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://dl.acm.org/citation.cfm?id=3291656.3291719",
abstract = "Low-precision floating-point arithmetic is a powerful
tool for accelerating scientific computing
applications, especially those in artificial
intelligence. Here, we present an investigation showing
that other high-performance computing (HPC)
applications can also harness this power. Specifically,
we use the general HPC problem, Ax = b, where A is a
large dense matrix, and a double precision (FP64)
solution is needed for accuracy. Our approach is based
on mixed-precision (FP16 $ \to $ FP64) iterative
refinement, and we generalize and extend prior advances
into a framework, for which we develop
architecture-specific algorithms and highly tuned
implementations. These new methods show how using
half-precision Tensor Cores (FP16-TC) for the
arithmetic can provide up to 4X speedup. This is due to
the performance boost that the FP16-TC provide as well
as to the improved accuracy over the classical FP16
arithmetic that is obtained because the GEMM
accumulation occurs in FP32 arithmetic.",
acknowledgement = ack-nhfb,
}
@Article{Higham:2018:DD,
author = "Nicholas Higham",
title = "Differentiation with(out) a difference",
journal = j-SIAM-NEWS,
volume = "51",
number = "5",
pages = "2",
year = "2018",
ISSN = "1557-9573",
ISSN-L = "1557-9573",
MRclass = "65D25 (41A80 65G50)",
MRnumber = "3823048",
bibdate = "Tue Jan 22 15:10:07 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Misc{Higham:2018:HPA,
author = "Nicholas J. Higham",
title = "Half Precision Arithmetic: fp16 Versus bfloat16",
howpublished = "Web site.",
day = "3",
month = dec,
year = "2018",
bibdate = "Sat Jan 19 18:43:15 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://nickhigham.wordpress.com/2018/12/03/half-precision-arithmetic-fp16-versus-bfloat16/",
abstract = "The 2008 revision of the IEEE Standard for
Floating-Point Arithmetic introduced a half precision
16-bit floating point format, known as fp16, as a
storage format. Various manufacturers have adopted fp16
for computation, using the obvious extension of the
rules for the fp32 (single precision) and fp64 (double
precision) formats. For example, fp16 is supported by
the NVIDIA P100 and V100 GPUs and the AMD Radeon
Instinct MI25 GPU, as well as the A64FX Arm processor
that will power the Fujitsu Post-K exascale computer.",
acknowledgement = ack-nhfb,
}
@Article{Higham:2018:RAB,
author = "Nicholas Higham",
title = "Rhapsodizing about {Bohemian} matrices",
journal = j-SIAM-NEWS,
volume = "51",
number = "10",
pages = "2",
year = "2018",
ISSN = "1557-9573",
ISSN-L = "1557-9573",
MRclass = "15B34",
MRnumber = "3929646",
bibdate = "Fri Jul 9 15:09:12 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Article{Higham:2018:SS,
author = "Nicholas Higham",
title = "Snap to structure",
journal = j-SIAM-NEWS,
volume = "51",
number = "1",
pages = "2",
year = "2018",
ISSN = "1557-9573",
ISSN-L = "1557-9573",
MRclass = "65G99 (68W30)",
MRnumber = "3823054",
bibdate = "Tue Jan 22 15:10:07 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Article{Higham:2018:TFD,
author = "Nicholas Higham",
title = "A timely focus on data science",
journal = j-SIAM-NEWS,
volume = "51",
number = "9",
pages = "2",
year = "2018",
ISSN = "1557-9573",
ISSN-L = "1557-9573",
MRclass = "68T01",
MRnumber = "3889491",
bibdate = "Fri Jul 9 15:09:43 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Article{Higham:2018:UN,
author = "Nicholas J. Higham",
title = "The Unwinding Number",
journal = j-SIAM-NEWS,
volume = "51",
number = "8",
pages = "2--2",
month = oct,
year = "2018",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
MRclass = "65E05 (68N15)",
MRnumber = "3823081",
bibdate = "Sat Oct 06 08:46:15 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://sinews.siam.org/Details-Page/the-unwinding-number",
abstract = "While Fortran 66 had a complex data type, this was not
true of most other early programming languages, such as
Algol 60. As a result, programmers had to write their
own procedures to implement complex arithmetic and
transcendental functions in terms of separately stored
real and imaginary parts. They quickly realized that
this is not a trivial task; in the early 1960s, it took
five published attempts over three years to obtain a
correct implementation of the complex logarithm in
Algol 60.",
acknowledgement = ack-nhfb,
}
@Article{Nadukandi:2018:CWK,
author = "Prashanth Nadukandi and Nicholas J. Higham",
title = "Computing the Wave-Kernel Matrix Functions",
journal = j-SIAM-J-SCI-COMP,
volume = "40",
number = "6",
pages = "A4060--A4082",
month = "????",
year = "2018",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/18M1170352",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F60 (15A60 41A21)",
MRnumber = "3884228",
MRreviewer = "Fazlollah Soleymani",
bibdate = "Tue Jan 22 15:10:07 2019",
bibsource = "http://epubs.siam.org/toc/sjoce3/40/6;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2018",
}
@Article{Anzt:2019:APB,
author = "Hartwig Anzt and Jack Dongarra and Goran Flegar and
Nicholas J. Higham and Enrique S. Quintana-Ort{\'\i}",
title = "Adaptive precision in block-{Jacobi} preconditioning
for iterative sparse linear system solvers",
journal = j-CCPE,
volume = "31",
number = "6",
pages = "e4460:1--e4460:??",
day = "25",
month = mar,
year = "2019",
CODEN = "CCPEBO",
DOI = "https://doi.org/10.1002/cpe.4460",
ISSN = "1532-0626 (print), 1532-0634 (electronic)",
ISSN-L = "1532-0626",
bibdate = "Thu Mar 28 08:07:56 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/ccpe.bib",
acknowledgement = ack-nhfb,
fjournal = "Concurrency and Computation: Practice and Experience",
journal-URL = "http://www.interscience.wiley.com/jpages/1532-0626",
onlinedate = "12 March 2018",
}
@TechReport{Blanchard:2019:MPB,
author = "Pierre Blanchard and Nicholas J. Higham and Florent
Lopez and Theo Mary and Srikara Pranesh",
title = "Mixed Precision Block Fused Multiply-Add: Error
Analysis and Application to {GPU} Tensor Cores",
type = "MIMS EPrint",
number = "2019.18",
institution = "Manchester Institute for Mathematical Sciences, School
of Mathematics, The University of Manchester",
address = "Manchester, UK",
day = "24",
month = sep,
year = "2019",
ISSN = "1749-9097",
bibdate = "Thu Dec 05 10:14:37 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://eprints.maths.manchester.ac.uk/2733/;
https://en.wikipedia.org/wiki/Bfloat16 floating-point
format",
abstract = "Computing units that carry out a fused multiply-add
(FMA) operation with matrix arguments, referred to as
tensor units by some vendors, have great potential for
use in scientific computing. However, these units are
inherently mixed precision and existing rounding error
analyses do not support them. We consider a mixed
precision block FMA that generalizes both the usual
scalar FMA and existing tensor units. We describe how
to exploit such a block FMA in the numerical linear
algebra kernels of matrix multiplication and LU
factorization and give rounding error analyses of both
kernels. An important application is to GMRES-based
iterative refinement with block FMAs, for which our
analysis provides new insight. Our framework is
applicable to the tensor core units in the NVIDIA Volta
and Turing GPUs. For these we compare matrix
multiplication and LU factorization with TC16 and TC32
forms of FMA, which differ in the precision used for
the output of the tensor cores. Our experiments on an
NVDIA V100 GPU confirm the predictions of the analysis
that the TC32 variant is much more accurate than the
TC16 one, while achieving almost the same
performance.",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; fused multiply-add; LU
factorization; matrix multiplication; rounding error
analysis, NVIDIA GPU; tensor cores",
}
@Article{Fasi:2019:APS,
author = "Massimiliano Fasi and Nicholas J. Higham",
title = "An arbitrary precision scaling and squaring algorithm
for the matrix exponential",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "40",
number = "4",
pages = "1233--1256",
year = "2019",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/18M1228876",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F60 (15A16)",
MRnumber = "4014393",
MRreviewer = "Ralf Zimmermann",
bibdate = "Fri Jul 9 15:12:06 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Hammarling:2019:CJH,
author = "Sven J. Hammarling and Nicholas J. Higham",
title = "Celebrating {James Hardy Wilkinson}",
journal = j-MATH-TODAY,
volume = "55",
number = "4",
pages = "131--131",
year = "2019",
ISSN = "1361-2042",
MRclass = "01A70",
MRnumber = "3967944",
bibdate = "Fri Jul 9 15:12:06 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Today",
journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
}
@Article{Higham:2019:NAP,
author = "Nicholas J. Higham and Theo Mary",
title = "A New Approach to Probabilistic Rounding Error
Analysis",
journal = j-SIAM-J-SCI-COMP,
volume = "41",
number = "5",
pages = "A2815--A2835",
month = "????",
year = "2019",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/18M1226312",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65G50 (60E15 65F05)",
MRnumber = "4002728",
MRreviewer = "A. Bultheel",
bibdate = "Tue Nov 5 05:24:19 MST 2019",
bibsource = "http://epubs.siam.org/toc/sjoce3/41/5;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/matlab.bib;
http://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "floating-point arithmetic; MATLAB; numerical linear
algebra; rounding error analysis",
onlinedate = "January 2019",
}
@Article{Higham:2019:NPE,
author = "Nicholas J. Higham and Theo Mary",
title = "A New Preconditioner that Exploits Low-Rank
Approximations to Factorization Error",
journal = j-SIAM-J-SCI-COMP,
volume = "41",
number = "1",
pages = "A59--A82",
month = "????",
year = "2019",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/18M1182802",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F22 (65F05 65F08 65F10 68W20)",
MRnumber = "3895124",
bibdate = "Thu Oct 10 06:58:01 MDT 2019",
bibsource = "http://epubs.siam.org/toc/sjoce3/41/1;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2019",
}
@Article{Higham:2019:SLP,
author = "Nicholas J. Higham and Srikara Pranesh",
title = "Simulating Low Precision Floating-Point Arithmetic",
journal = j-SIAM-J-SCI-COMP,
volume = "41",
number = "5",
pages = "C585--C602",
month = "????",
year = "2019",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/19M1251308",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F05 (65G50 65Y04)",
MRnumber = "4024753",
MRreviewer = "Jin Yun Yuan",
bibdate = "Tue Nov 5 05:24:19 MST 2019",
bibsource = "http://epubs.siam.org/toc/sjoce3/41/5;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/matlab.bib;
http://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "bfloat16; bit flips; directed rounding; floating-point
arithmetic; fp16; half precision; IEEE arithmetic; low
precision; MATLAB; mixed precision; round to nearest;
rounding error analysis; simulation; stochastic
rounding; subnormal numbers",
onlinedate = "January 2019",
}
@Article{Higham:2019:SMH,
author = "Nicholas J. Higham and Srikara Pranesh and Mawussi
Zounon",
title = "Squeezing a Matrix into Half Precision, with an
Application to Solving Linear Systems",
journal = j-SIAM-J-SCI-COMP,
volume = "41",
number = "4",
pages = "A2536--A2551",
month = "????",
year = "2019",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/18M1229511",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F35 (65F05 65F08 65F10 65G50)",
MRnumber = "3987532",
MRreviewer = "A. Bultheel",
bibdate = "Thu Oct 10 06:58:08 MDT 2019",
bibsource = "http://epubs.siam.org/toc/sjoce3/41/4;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/matlab.bib;
http://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "diagonal scaling; fp16; GMRES; half precision
arithmetic; iterative refinement; linear system;
MATLAB; mixed precision; overflow; preconditioning;
subnormal numbers; underflow",
onlinedate = "January 2019",
}
@Article{Blanchard:2020:CFA,
author = "Pierre Blanchard and Nicholas J. Higham and Theo
Mary",
title = "A Class of Fast and Accurate Summation Algorithms",
journal = j-SIAM-J-SCI-COMP,
volume = "42",
number = "3",
pages = "A1541--A1557",
month = "????",
year = "2020",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/19M1257780",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65B10 (65F05 65G50)",
MRnumber = "4094754",
MRreviewer = "S. Hitotumatu",
bibdate = "Fri Mar 12 11:39:57 MST 2021",
bibsource = "http://epubs.siam.org/toc/sjoce3/42/3;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
abstract = "The need to sum floating-point numbers is ubiquitous
in scientific computing. Standard recursive summation
of $n$ summands, often implemented in a blocked form,
has a backward error bound proportional to $ n u$,
where $u$ is the unit roundoff. With the growing
interest in low precision floating-point arithmetic and
ever increasing $n$ in applications, computed sums are
more likely to have insufficient accuracy. We propose a
class of summation algorithms called FABsum (for fast
and accurate block summation'') that applies a fast
summation algorithm (such as recursive summation)
blockwise and then sums the partial sums using an
accurate summation algorithm (such as compensated
summation, or recursive summation in higher precision).
We give a rounding error analysis to show that FABsum
with a fixed block size $b$ has a backward error bound
$ (b + 1)u + O(u^2)$, which is independent of $n$ to
first order. Our computational experiments show that
with a suitable choice of $b$ (independent of $n$)
FABsum can deliver substantially more accurate results
than blocked recursive summation, with only a modest
drop in performance. FABsum is especially attractive
for low precisions, where it can provide correct digits
for much larger $n$ than recursive summation.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
onlinedate = "January 2020",
}
@Article{Blanchard:2020:MPB,
author = "Pierre Blanchard and Nicholas J. Higham and Florent
Lopez and Theo Mary and Srikara Pranesh",
title = "Mixed precision block fused multiply-add: error
analysis and application to {GPU} tensor cores",
journal = j-SIAM-J-SCI-COMP,
volume = "42",
number = "3",
pages = "C124--C141",
year = "2020",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/19M1289546",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F05 (65G50 65Y04 68M07)",
MRnumber = "4103291",
bibdate = "Fri Jul 9 15:12:06 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Carson:2020:TPG,
author = "Erin Carson and Nicholas J. Higham and Srikara
Pranesh",
title = "Three-precision {GMRES}-based iterative refinement for
least squares problems",
journal = j-SIAM-J-SCI-COMP,
volume = "42",
number = "6",
pages = "A4063--A4083",
year = "2020",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/20M1316822",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F05 (65F08 65F20)",
MRnumber = "4188846",
bibdate = "Fri Jul 9 15:12:06 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Dongarra:2020:NAH,
author = "Jack Dongarra and Laura Grigori and Nicholas J.
Higham",
title = "Numerical algorithms for high-performance
computational science",
journal = j-PHILOS-TRANS-R-SOC-LOND-SER-A,
volume = "378",
number = "2166",
pages = "20190066:1--20190066:18",
year = "2020",
DOI = "https://doi.org/10.1098/rsta.2019.0066",
ISSN = "1364-503X (print), 1471-2962 (electronic)",
MRclass = "65Y10",
MRnumber = "4072450",
bibdate = "Fri Jul 9 15:12:06 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
ajournal = "Philos. Trans. Roy. Soc. A",
fjournal = "Philosophical Transactions of the Royal Society A.
Mathematical, Physical and Engineering Sciences",
}
@Article{Haidar:2020:MPI,
author = "Azzam Haidar and Harun Bayraktar and Stanimire Tomov
and Jack Dongarra and Nicholas J. Higham",
title = "Mixed-precision iterative refinement using tensor
cores on {GPUs} to accelerate solution of linear
systems",
journal = j-PROC-R-SOC-LOND-SER-A,
volume = "476",
number = "2243",
pages = "20200110:1--2020011030",
year = "2020",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.2020.0110",
ISSN = "1364-5021 (print), 1471-2946 (electronic)",
ISSN-L = "1364-5021",
MRclass = "65F10 (65Y10)",
MRnumber = "4187936",
bibdate = "Fri Jul 9 15:12:06 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society of London. Series A",
journal-URL = "http://rspa.royalsocietypublishing.org/",
}
@Book{Higham:2020:HWM,
author = "Nicholas J. Higham",
title = "Handbook of Writing for the Mathematical Sciences",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxi + 353",
year = "2020",
DOI = "https://doi.org/10.1137/1.9781611976106",
ISBN = "91-611-9760-9-X (paperback), 1-61197-610-3 (e-book)",
ISBN-13 = "91-611-9760-9-X (paperback), 978-1-61197-610-6
(e-book)",
LCCN = "QA42 .H54 2020",
MRclass = "00A20",
MRnumber = "4050520",
bibdate = "Fri Jul 9 15:12:06 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
abstract = "{{\booktitle{Handbook of Writing for the Mathematical
Sciences}}} provides advice on all aspects of
scientific writing, with a particular focus on writing
mathematics. Its readable style and handy format,
coupled with an extensive bibliography and
comprehensive index, make it useful for everyone from
undergraduates to seasoned professionals. This third
edition revises, updates, and expands the best-selling
second edition to reflect modern writing and publishing
practices and builds on the author's extensive
experience in writing and speaking about mathematics.
Key features are coverage of fundamentals of writing,
including English usage, revising a draft, and writing
when your first language is not English; thorough
treatment of mathematical writing, including how to
choose notation, how to choose between words and
symbols, and how to format equations; many tips for
exploiting \LaTeX{} and \BibTeX{}; advice on how to
write and publish a paper, covering the entire
publication process; and anecdotes, quotes, and unusual
facts that enliven the presentation. The new edition
has been reorganized to make the book easier to use for
reference; treats modern developments in publishing
such as open access, DOIs, and ORCID; has a new chapter
on workflow covering text editors, markup languages,
version control, and much more; has a new chapter that
discusses the principles of indexing and how to prepare
an index in \LaTeX; has a new chapter on reviewing a
paper, book proposal, or book; has a new chapter
``Writing a Book'' that includes advice on choosing a
publisher and \LaTeX tips particular to books; contains
more on poster design, and discusses e-posters and the
poster blitz; and has a new chapter giving advice on
writing a blog post.",
acknowledgement = ack-nhfb,
remark = "Third edition of \cite{Higham:1998:HWM} (MR1223778).",
tableofcontents = "General principles \\
Mathematical writing \\
English usage \\
The writer's bookshelf \\
When English is a foreign language \\
Writing a paper \\
Revising a draft \\
\TeX{}, \LaTeX{}, and \BibTeX{} \\
Workflow \\
Publishing a paper \\
Refereeing and reviewing \\
Writing a talk \\
Giving a talk \\
Preparing a poster \\
Writing and defending a thesis \\
Writing a book \\
Preparing an index \\
Writing a blog post \\
Information sources",
}
@Article{Higham:2020:SPB,
author = "Nicholas J. Higham and Theo Mary",
title = "Sharper probabilistic backward error analysis for
basic linear algebra kernels with random data",
journal = j-SIAM-J-SCI-COMP,
volume = "42",
number = "5",
pages = "A3427--A3446",
year = "2020",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/20M1314355",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F35 (60E15 65F05 65G50)",
MRnumber = "4165945",
bibdate = "Fri Jul 9 15:12:06 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Abdelfattah:2021:SBB,
author = "Ahmad Abdelfattah and Timothy Costa and Jack Dongarra
and Mark Gates and Azzam Haidar and Sven Hammarling and
Nicholas J. Higham and Jakub Kurzak and Piotr Luszczek
and Stanimire Tomov and Mawussi Zounon",
title = "A Set of Batched Basic Linear Algebra Subprograms and
{LAPACK} Routines",
journal = j-TOMS,
volume = "47",
number = "3",
pages = "21:1--21:23",
month = jun,
year = "2021",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3431921",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Jun 27 07:42:02 MDT 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3431921",
abstract = "This article describes a standard API for a set of
Batched Basic Linear Algebra Subprograms (Batched BLAS
or BBLAS). The focus is on many independent BLAS
operations on small matrices that are grouped together
and processed by a single routine, called a Batched
BLAS routine. The matrices are grouped together in
uniformly sized groups, with just one group if all the
matrices are of equal size. The aim is to provide more
efficient, but portable, implementations of algorithms
on high-performance many-core platforms. These include
multicore and many-core CPU processors, GPUs and
coprocessors, and other hardware accelerators with
floating-point compute facility. As well as the
standard types of single and double precision, we also
include half and quadruple precision in the standard.
In particular, half precision is used in many very
large scale applications, such as those associated with
machine learning.",
acknowledgement = ack-nhfb,
articleno = "21",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Blanchard:2021:ACL,
author = "Pierre Blanchard and Desmond J. Higham and Nicholas J.
Higham",
title = "Accurately computing the log-sum-exp and softmax
functions",
journal = j-IMA-J-NUMER-ANAL,
volume = "41",
number = "4",
pages = "2311--2330",
month = oct,
year = "2021",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/draa038",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
bibdate = "Sat Oct 23 16:14:21 MDT 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib",
URL = "http://academic.oup.com/imajna/article/41/4/2311/5893596",
abstract = "Evaluating the log-sum-exp function or the softmax
function is a key step in many modern data science
algorithms, notably in inference and classification.
Because of the exponentials that these functions
contain, the evaluation is prone to overflow and
underflow, especially in low-precision arithmetic.
Software implementations commonly use alternative
formulas that avoid overflow and reduce the chance of
harmful underflow, employing a shift or another
rewriting. Although mathematically equivalent, these
variants behave differently in floating-point
arithmetic and shifting can introduce subtractive
cancellation. We give rounding error analyses of
different evaluation algorithms and interpret the error
bounds using condition numbers for the functions. We
conclude, based on the analysis and numerical
experiments, that the shifted formulas are of similar
accuracy to the unshifted ones, so can safely be used,
but that a division-free variant of softmax can suffer
from loss of accuracy.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Connolly:2021:SRP,
author = "Michael P. Connolly and Nicholas J. Higham and Theo
Mary",
title = "Stochastic rounding and its probabilistic backward
error analysis",
journal = j-SIAM-J-SCI-COMP,
volume = "43",
number = "1",
pages = "A566--A585",
year = "2021",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/20M1334796",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65G50 (60G42 65F35)",
MRnumber = "4214365",
bibdate = "Fri Jul 9 15:12:06 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Fasi:2021:GES,
author = "Massimiliano Fasi and Nicholas J. Higham",
title = "Generating extreme-scale matrices with specified
singular values or condition number",
journal = j-SIAM-J-SCI-COMP,
volume = "43",
number = "1",
pages = "A663--A684",
year = "2021",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/20M1327938",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F18 (65F35 65Y05)",
MRnumber = "4218408",
bibdate = "Fri Jul 9 15:12:06 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Fasi:2021:MTI,
author = "Massimiliano Fasi and Nicholas J. Higham",
title = "Matrices with Tunable Infinity-Norm Condition Number
and No Need for Pivoting in {$ L U $} Factorization",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "42",
number = "1",
pages = "417--435",
month = "????",
year = "2021",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/20M1357238",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F35 (65Y05)",
MRnumber = "4232450",
bibdate = "Fri Jul 9 15:12:06 2021",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/42/1;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2021",
}
@Article{Higham:2021:ELP,
author = "Nicholas J. Higham and Srikara Pranesh",
title = "Exploiting lower precision arithmetic in solving
symmetric positive definite linear systems and least
squares problems",
journal = j-SIAM-J-SCI-COMP,
volume = "43",
number = "1",
pages = "A258--A277",
year = "2021",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/19M1298263",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F05 (65F08 65F10 65F35)",
MRnumber = "4201445",
bibdate = "Fri Jul 9 15:12:06 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Higham:2021:IMF,
author = "Nicholas J. Higham and Matthew C. Lettington and Karl
Michael Schmidt",
title = "Integer matrix factorisations, superalgebras and the
quadratic form obstruction",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "622",
pages = "250--267",
year = "2021",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2021.03.028",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15B36 (05B15 11E12 15A15 15A23 15A30)",
MRnumber = "4241259",
bibdate = "Fri Jul 9 15:12:06 2021",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Higham:2021:MDF,
author = "Nicholas J. Higham and Xiaobo Liu",
title = "A Multiprecision Derivative-Free {Schur--Parlett}
Algorithm for Computing Matrix Functions",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "42",
number = "3",
pages = "1401--1422",
month = "????",
year = "2021",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/20M1365326",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F60",
MRnumber = "4313845",
bibdate = "Tue Jan 18 10:51:55 MST 2022",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/42/3;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2021",
}
@Article{Higham:2021:RMG,
author = "Desmond J. Higham and Nicholas J. Higham and Srikara
Pranesh",
title = "Random Matrices Generating Large Growth in {$ L U $}
Factorization with Pivoting",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "42",
number = "1",
pages = "185--201",
month = "????",
year = "2021",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/20M1338149",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F05 (15B52 65F35)",
MRnumber = "4207902",
bibdate = "Fri Jul 9 15:12:06 2021",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/42/1;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2021",
}
@Article{Higham:2022:AEM,
author = "Nicholas J. Higham and Mantas Mikaitis",
title = "\pkg{Anymatrix}: an extensible {MATLAB} matrix
collection",
journal = j-NUMER-ALGORITHMS,
volume = "90",
number = "3",
pages = "1175--1196",
month = jul,
year = "2022",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-021-01226-2",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Thu Jun 9 09:50:52 MDT 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/matlab.bib;
http://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "https://link.springer.com/article/10.1007/s11075-021-01226-2",
acknowledgement = ack-nhfb,
ajournal = "Numer. Algorithms",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Higham:2022:MPA,
author = "Nicholas J. Higham and Theo Mary",
title = "Mixed precision algorithms in numerical linear
algebra",
journal = j-ACTA-NUMERICA,
volume = "31",
pages = "347--414",
month = may,
year = "2022",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S0962492922000022",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
bibdate = "Wed Jun 15 09:10:34 MDT 2022",
bibsource = "http://journals.cambridge.org/action/displayIssue?jid=ANU&volumeId=31&issueId=00;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
URL = "https://www.cambridge.org/core/journals/acta-numerica/article/mixed-precision-algorithms-in-numerical-linear-algebra/43CA701BA29251B5790C653E66F46197",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
onlinedate = "09 June 2022",
}
@Article{Higham:2022:SBL,
author = "Nicholas J. Higham and Theo Mary",
title = "Solving block low-rank linear systems by {$ L U $}
factorization is numerically stable",
journal = j-IMA-J-NUMER-ANAL,
volume = "42",
number = "2",
pages = "951--980",
month = apr,
year = "2022",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/drab020",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
bibdate = "Sat Apr 23 13:25:36 MDT 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib",
URL = "http://academic.oup.com/imajna/article/42/2/951/6238550",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Proceedings{Iserles:1987:SAN,
editor = "A. Iserles and M. J. D. Powell",
booktitle = "{State of the Art in Numerical Analysis. Proceedings
of the Joint IMA\slash SIAM Conference held at the
University of Birmingham, 14--18 April 1986}",
title = "{State of the Art in Numerical Analysis. Proceedings
of the Joint IMA\slash SIAM Conference held at the
University of Birmingham, 14--18 April 1986}",
volume = "9",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "x + 719",
year = "1987",
ISBN = "0-19-853614-3",
ISBN-13 = "978-0-19-853614-7",
LCCN = "QA297.J65 1986",
bibdate = "Mon Sep 9 14:56:14 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "The Institute of Mathematics and Its Applications
conference series; new series",
URL = "http://www.gbv.de/dms/hbz/toc/ht002967923.pdf;
http://zbmath.org/?q=an:0611.00024",
ZMnumber = "0611.00024",
acknowledgement = ack-nhfb,
confdate = "14--18 April 1986",
conflocation = "Birmingham, UK",
confsponsor = "Inst. Math. Appl.; SIAM",
pubcountry = "UK",
tableofcontents = "Contributors / / xiii \\
1. Eigenvalue problems / J. H. Wilkinson / 1 \\
2. Numerical linear algebra in statistical computing /
N. J. Higham and G. W. Stewart / 41 \\
3. Sparse matrices / J. K. Reid / 59 \\
4. Multivariate approximation / Carl de Boor / 87 \\
5. Data approximation by splines in one and two
independent variables / M. G. Cox / 111 \\
6. Methods for best approximation and regression
problems / G. A. Watson / 139 \\
7. Branch cuts for complex elementary functions / W.
Kahan / 165 \\
8. Recent developments in linear and quadratic
programming / R. Fletcher / 213 \\
9. Solving systems of nonlinear equations by tensor
methods / R. B. Schnabel and P. D. Frank / 245 \\
10. Numerical methods for bifurcation problems / A. D.
Jepson and A. Spence / 273 \\
11. On the iterative solution of differential and
integral equations using secant updating techniques /
A. Griewank / 299 \\
12. Methods for nonlinear constraints in optimization
calculations / M. J. D. Powell / 325 \\
13. The influence of vector and parallel processors on
numerical analysis / I. S. Duff / 359 \\
14. Developments in stability theory for ordinary
differential equations / J. D. Lambert / 409 \\
15. Stiff ODE initial value problems and their solution
/ A. R. Curtis / 433 \\
16. Order stars and stability / G. Wanner / 451 \\
17. The state of the art in the numerical treatment of
integral equations / C. T. H. Baker / 473 \\
18. Strongly elliptic boundary integral equations / W.
L. Wendland / 511 \\
19. Collocation methods for one-dimensional Fredholm
and Volterra integral equations / H. Brunner / 563 \\
20. Numerical methods for free and moving boundary
problems / C. W. Cryer / 601 \\
21. Multigrid methods for elliptic equations / J. Walsh
/ 623 \\
22. Galerkin finite element methods and their
generalizations / K. W. Morton / 645 \\
23. Recent developments in the numerical solution of
nonlinear conservation laws / S. Osher and P. K. Sweby
/ 681 \\
Index / 701",
}
@Article{Dongarra:1990:ASL,
author = "Jack J. Dongarra and Jeremy {Du Croz} and Sven
Hammarling and Iain Duff",
title = "{Algorithm 679}: {A} Set of {Level 3 Basic Linear
Algebra Subprograms}: Model Implementation and Test
Programs",
journal = j-TOMS,
volume = "16",
number = "1",
pages = "18--28",
month = mar,
year = "1990",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/77626.77627",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Mar 22 15:39:54 MST 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "See also
\cite{Higham:1990:EFM,Demmel:1992:SBA,Dayde:1994:PBI}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p18-dongarra/;
http://www.netlib.org/utk/people/JackDongarra/PAPERS/ALGORITHM-679-A-Set-of-Level-3-BLAS.pdf",
acknowledgement = ack-nhfb,
classcodes = "C4140 (Linear algebra); C7310 (Mathematics)",
corpsource = "Oak Ridge Nat. Lab., TN, USA",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
keywords = "computers; Fortran 77; high-performance; level 3 basic
linear algebra subprograms; mathematics computing;
matrix algebra; matrix-matrix operations; portable;
program testing; subroutines; test programs",
treatment = "P Practical",
}
@Proceedings{Meyer:1993:LAM,
editor = "C. D. (Carl Dean) Meyer and Robert J. Plemmons",
booktitle = "{Linear algebra, Markov chains, and queueing models:
[\ldots{} some of the lectures given at the Workshop
Linear Algebra, Markov Chains, and Queueing Models held
January 13--17, 1992, as part of the Year of Applied
Linear Algebra at the Institute for Mathematics and its
Applications]}",
title = "{Linear algebra, Markov chains, and queueing models:
[\ldots{} some of the lectures given at the Workshop
Linear Algebra, Markov Chains, and Queueing Models held
January 13--17, 1992, as part of the Year of Applied
Linear Algebra at the Institute for Mathematics and its
Applications]}",
volume = "48",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 294",
year = "1993",
ISBN = "0-387-94085-5 (New York), 3-540-94085-5 (Berlin)",
ISBN-13 = "978-0-387-94085-4 (New York), 978-3-540-94085-2
(Berlin)",
LCCN = "QA184 .L545 1993",
bibdate = "Wed May 28 17:58:34 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
z3950.loc.gov:7090/Voyager",
series = "The IMA volumes in mathematics and its applications",
URL = "http://catalog.hathitrust.org/api/volumes/oclc/28182134.html;
http://www.gbv.de/dms/ilmenau/toc/126000387.PDF;
http://www.zentralblatt-math.org/zmath/en/search/?an=0779.00020",
acknowledgement = ack-nhfb,
subject = "Algebras, Linear; Congresses; Markov processes;
Queuing theory",
tableofcontents = "Error bounds for the computation of null vectors
with applications to Markov chains / Jesse L. Barlow
\\
The influence of nonnormality on matrix computations /
Fran{\c{c}}oise Chatelin \\
Componentwise error analysis for stationary iterative
methods / Nicholas J. Higham and Philip A. Knight \\
The character of a finite Markov chain / Carl D. Meyer
\\
Gaussian elimination, perturbation theory, and Markov
chains / G. W. Stewart \\
Algorithms for periodic Markov chains / Fran{\c{c}}ois
Bonhoure, Yves Dallery, and William J. Stewart \\
Iterative methods for queueing networks with irregular
state-spaces / Raymond H. Chan \\
Analysis of $p$-cyclic iterations for Markov chains /
Apostolos Hadjidimos and Robert J. Plemmons \\
Iterative methods for finding the stationary vector for
Markov chains / Dianne P. O'Leary \\
Local convergence of (exact and inexact) iterative
aggregation / Daniel B. Szyld \\
Automated generation and analysis of Markov reward
models using stochastic reward nets / Gianfranco Ciardo
\ldots{} [et al.] \\
Means and variances in Markov reward systems / Winfried
K. Grassman \\
A direct algorithm for computing the stationary
distribution of a $p$-cyclic Markov chain / Daniel P.
Heyman \\
Approximate analysis of a discrete-time queueing model
of the shared buffer ATM switch / S. Hong, H. G.
Perros, and H. Yamashita \\
Algorithms for infinite Markov chains with repeating
columms / Guy Latouche \\
Cray-2 memory organization and interprocessor memory
contention / Robert W. Numrich",
}
@Proceedings{Moonen:1993:LAL,
editor = "Marc S. Moonen and Gene H. Golub and Bart L. R. {De
Moor}",
booktitle = "{Linear Algebra for Large Scale and Real-Time
Applications: Proceedings of the NATO Advanced Study
Institute, Leuven, Belgium, August 3--14, 1992}",
title = "{Linear Algebra for Large Scale and Real-Time
Applications: Proceedings of the NATO Advanced Study
Institute, Leuven, Belgium, August 3--14, 1992}",
volume = "232",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "ix + 435",
year = "1993",
ISBN = "0-7923-2151-0",
ISBN-13 = "978-0-7923-2151-4",
LCCN = "QA185.D37 L56 1993",
MRclass = "65-06 (65Fxx 65Y05)",
MRnumber = "94e:65009",
bibdate = "Mon Jan 15 17:53:04 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib",
series = "NATO ASI series. Series E, Applied sciences",
URL = "http://catdir.loc.gov/catdir/enhancements/fy0823/92046135-d.html;
http://www.gbv.de/dms/hbz/toc/ht004938330.pdf;
http://zbmath.org/?q=an:0810.00029",
ZMnumber = "0810.00029",
abstract = "In recent years there has been great interest in large
scale and real-time matrix computations; these
computations arise in a variety of fields, such as
computer graphics, imaging, speech and image
processing, telecommunication, biomedical signal
processing, optimization and so on. This volume, which
is an outgrowth of a NATO ASI, held at Leuven, Belgium,
August 1992, gives an account of recent research
advances in numerical techniques used in large scale
and real-time computations and their implementation on
high performance computers.",
acknowledgement = ack-nhfb,
tableofcontents = "Preface / / xi \\
Invited Lectures / / 1 \\
Large scale structural analysis on massively parallel
computers / P. E. Bj{\o}rstad and J. Cook / 3 \\
Data-parallel BLAS as a basis for LAPACK on massively
parallel computers / P. E. Bj{\o}rstad and T.
S{\o}revik / 13 \\
a Large-scale nonlinear constrained optimization / A.
R. Conn, N. Gould and Ph. L. Toint / 21 \\
Trading off parallelism and numerical stability / J. W.
Demmel / 49 \\
Subband filtering: CORDIC modulation and systolic
quadrature mirror filter tree / E. F. Deprettere / 69
\\
A parallel image rendering algorithm and architecture
based on ray tracing and radiosity shading / E. F.
Deprettere and L.-S. Shen / 91 \\
Reduction and approximation of linear computational
circuits / P. Dewilde and A.-J. van der Veen / 109 \\
The look-ahead Lanczos process for large nonsymmetric
matrices and related algorithms / R. W. Freund / 137
\\
Case studies of real-time processing in robotics / W.
M. Gentleman / 165 \\
Adaptive signal processing with emphasis on QRD-least
squares lattice / S. Haykin / 183 \\
A direct method for reordering eigenvalues in the
generalized real Schur form of a regular matrix pair
(A, B) / B. K{\aa}gstr{\"o}m / 195 \\
Block shift invariance and efficient system
identification algorithms / N. Kalouptsidis / 219 \\
Computing the singular value decomposition on a
fat-tree architecture / T. J. Lee, F. T. Luk and D. L.
Boley / 231 \\
A new matrix decomposition for signal processing / F.
T. Luk and S. Qiao / 241 \\
The linear algebra of perfect reconstruction filtering
/ M. Stewart and G. Cybenko / 249 \\
Determining rank in the presence of error / G. W.
Stewart / 275 \\
Approximation with Kronecker products / C. F. Van Loan
and N. Pitsianis / 293 \\
Some linear algebra issues in large-scale optimization
/ M. H. Wright / 315 \\
Contributed Lectures / / 339 \\
Direct and inverse unitary eigenproblems in signal
processing: an overview / G. S. Ammar, W. B. Gragg and
L. Reichel / 341 \\
Block implementations of the symmetric QR and Jacobi
algorithms / P. Arbenz and M. Oettli / 345 \\
Linear algebra for large-scale information retrieval
applications / M. W. Berry / 347 \\
Matched filter vs. least-squares approximation / L. H.
J. Bierens / 349 \\
Reordering diagonal blocks in real Schur form / A. W.
Bojanczyk and P. Van Dooren / 351 \\
Placing zeroes and the Kronecker canonical form / D. L.
Boley and P. Van Dooren / 353 \\
Analysis of the recursive least squares lattice
algorithm / J. R. Bunch and R. C. LeBorne / 355 \\
Adaptive Chebyshev iteration based on modified moments
/ D. Calvetti, G. H. Golub and L. Reichel / 357 \\
Continuous realization methods and their applications /
M. T. Chu / 359 \\
Asymptotic behavior of orthogonal polynomials / T. Dehn
/ 361 \\
CADCS and parallel computing / F. Dumortier, A. Van
Cauwenberghe and L. Boullart / 363 \\
Eigenvalue roulette and random test matrices / A.
Edelman / 365 \\
On numerical methods for unitary eigenvalue problems /
H. Fa{\sas}bender / 369 \\
Accurate singular values and differential qd algorithms
/ K. V. Fernando and B. N. Parlett / 371 \\
Orthogonal projection and total least squares / R. D.
Fierro and J. R. Bunch / 375 \\
Gauss quadratures associated with the Arnoldi process
and the Lanczos algorithm / R. W. Freund and M.
Hochbruck / 377 \\
An implementation of the QMR method based on coupled
two-term recurrences / R. W. Freund and N. M. Nachtigal
/ 381 \\
Computationally efficient homotopies for the H 2 model
order reduction problem / Y. Ge, L. T. Watson, E. G.
Collins, Jr. and L. D. Davis / 385 \\
A fast algorithm for QR decomposition of Toeplitz
matrices / G. O. Glentis / 387 \\
Unitary Hessenberg methods for Toeplitz approximations
and applications / Ch. He and A. Bunse-Gerstner / 389
\\
Perturbation theory and backward error for $A X - X B =
C$ / N. J. Higham / 391 \\
Fast transforms and elliptic problems / T. Huckle / 393
\\
An interior-point method for minimizing the maximum
eigenvalue of a linear combination of matrices / F.
Jarre / 395 \\
The lattice-ladder with generalized forgetting / J.
Kadlec / 397 \\
Solving a least squares problem with boundary
constraints / L. Kaufman / 399 \\
Estimating the extremal eigenvalues and condition
number by the Lanczos algorithm with a random start /
J. Kuczy{\'n}ski and H. Wo{\'z}niakowski / 401 \\
A generalized ADI iterative method / N. Levenberg and
L. Reichel / 403 \\
Quaternions and the symmetric eigenvalue problem / N.
Mackey / 405 \\
Application of the Gauss-Seidel iteration to the RLS
algorithm / {\"O}. Morg{\"u}l and A. Mala{\c{s}} / 407
\\
Ranks of submatrices of a matrix and its inverse / C.
C. Paige and M. Wei / 409 \\
A QRD-based least-squares algorithm for multipulse
antenna array signal processing / I. K. Proudler / 411
\\
On displacement structures for covariance matrices and
lossless functions / P. A. Regalia and F. Desbouvries /
413 \\
Application of vector extrapolation and conjugate
gradient type methods to the semiconductor device
problem / W. H. A. Schilders / 415 \\
Accurate symmetric eigenreduction by a Jacobi method /
I. Slapni{\v{c}}ar / 417 \\
The order-recursive Chandrasekhar equations for fast
square-root Kalman filtering / D. T. M. Slock / 419 \\
Hybrid iterative methods based on Faber polynomials /
G. Starke / 421 \\
Aspects of implementing a 'C' matrix library / D. E.
Stewart / 423 \\
Intermediate fill-in in sparse QR decomposition / M.
T{\r{u}}ma / 425 \\
Shifting strategies for the parallel QR algorithm / D.
S. Watkins / 427 \\
List of Participants / / 429 \\
Authors Index / / 437",
}
@Article{Dayde:1994:PBI,
author = "Michael J. Dayd{\'e} and Iain S. Duff and Antoine
Petitet",
title = "A Parallel Block Implementation of Level-3 {BLAS} for
{MIMD} Vector Processors",
journal = j-TOMS,
volume = "20",
number = "2",
pages = "178--193",
month = jun,
year = "1994",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Sep 09 13:52:29 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "See
\cite{Dongarra:1990:ASL,Higham:1990:EFM,Demmel:1992:SBA}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
keywords = "algorithms; Level-3 BLAS; matrix-matrix kernels;
measurement; parallelization; performance;
vectorization",
subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]:
Numerical Algorithms and Problems--computations on
matrices; G.1.0 [Numerical Analysis]:
General--numerical algorithms; G.1.3 [Numerical
Analysis]: Numerical Linear Algebra--linear systems
(direct and iterative methods); G.4 [Mathematics of
Computing]: Mathematical Software--certification and
testing; efficiency; portability; reliability and
robustness; verification",
}
@Proceedings{Duff:1997:SAN,
editor = "Iain S. Duff and G. Alistair Watson",
booktitle = "The state of the art in numerical analysis",
title = "The state of the art in numerical analysis",
volume = "63",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xiv + 562",
year = "1997",
ISBN = "0-19-850014-9",
ISBN-13 = "978-0-19-850014-8",
LCCN = "QA297.S775 1997",
MRclass = "65-06 (00B25)",
MRnumber = "MR1628339 (99a:65008)",
bibdate = "Thu Sep 16 11:59:48 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
http://www.math.utah.edu/pub/bibnet/authors/g/gould-nicholas-ian.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
http://www.math.utah.edu/pub/tex/bib/numana1990.bib",
note = "Based on the proceedings of a conference on the state
of the art in numerical analysis. Organized by the
Institute of Mathematics and Its Applications and held
at York University in April 1996.",
series = "The Institute of Mathematics and Its Applications
conference series: new series",
URL = "https://global.oup.com/academic/product/the-state-of-the-art-in-numerical-analysis-9780198500148",
acknowledgement = ack-nhfb,
tableofcontents = "1. Recent Developments in Dense Numerical Linear
Algebra / N. J. Higham \\
2. Sparse Numerical Linear Algebra: Direct Methods and
Preconditioning / I. S. Duff \\
3. Closer to the Solution: Iterative Linear Solvers /
G. H. Golub and H. A. van der Vorst \\
4. 150 Years Old and Still Alive: Eigenproblems / H. A.
van der Vorst and G. H. Golub \\
5. Geometric Integration / J. M. Sanz-Serna \\
6. Convergence and Stability in the Numerical
Approximation of Dynamical Systems / A. Stuart \\
7. Beyond the Classical Theory of Computational
Ordinary Differential Equations / A. Iserles \\
8. Numerical Analysis of Volterra Functional and
Integral Equations / C. T. H. Baker \\
9. The Numerical Solution of Boundary Integral
Equations / K. E. Atkinson \\
10. Aspects of Approximation with Emphasis on the
Univariate Case / G. A. Watson \\
11. A Review of Methods for Multivariable Interpolation
at Scattered Data Points / M. J. D. Powell \\
12. Large Scale Unconstrained Optimization / J. Nocedal
\\
13. Interior Point Methods for Linear and Nonlinear
Programming / D. F. Shanno and E. M. Simantiraki \\
14. Methods for Nonlinear Constraints in Optimization
Calculations / A. R. Conn, N. I. M. Gould and Ph. L.
Toint \\
15. Stabilization Techniques and Subgrid Scales
Capturing, F. Brezzi, L. P. Franca / T. J. R. Hughes
and A. Russo \\
16. Approximation of Curvature Dependent Interface
Motion / C. M. Elliott \\
17. Finite Element Methods for Hyperbolic Problems: a
Posteriori Error Analysis and Adaptivity / E. S{\"u}li
and P. Houston \\
18. Approximation of Multidimensional Hyperbolic
Partial Differential Equations / K. W. Morton \\
19. Algorithms in Tomography / F. Natterer \\
20. Partial Differential Equations and Image Iterative
Filtering / F. Guichard and J.-M. Morel",
}
@Book{Ainsworth:1999:GSG,
editor = "Mark Ainsworth and Jeremy Levesley and Marco
Marletta",
title = "The Graduate Student's Guide to Numerical Analysis
'98: Lecture Notes from the {VIII EPSRC Summer School
in Numerical Analysis}",
volume = "26",
publisher = pub-SPRINGER,
address = pub-SPRINGER:adr-B,
pages = "x + 250",
year = "1999",
ISBN = "3-540-65752-5 (hardcover)",
ISBN-13 = "978-3-540-65752-1 (hardcover)",
ISSN = "0179-3632",
LCCN = "QA 297 G67 1999",
bibdate = "Wed Nov 3 09:30:14 MST 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "The Eighth EPSRC Numerical Analysis Summer School was
held at the University of Leicester from the 5th to the
17th of July, 1998.",
series = "Springer series in computational mathematics",
acknowledgement = ack-nhfb,
keywords = "numerical analysis",
}
@Proceedings{Higham:1998:NAP,
editor = "D. J. (Desmond J.) Higham and G. A. Watson and D. F.
(David Francis) Griffiths",
booktitle = "{Numerical analysis 1997: Proceedings of the 17th
Dundee Biennial Conference, June 24--27, 1997}",
title = "{Numerical analysis 1997: proceedings of the 17th
Dundee Biennial Conference, June 24--27, 1997}",
volume = "380",
publisher = pub-LONGMAN-ST,
address = pub-LONGMAN-ST:adr,
pages = "254",
year = "1998",
ISBN = "0-582-31261-2 (paperback)",
ISBN-13 = "978-0-582-31261-6 (paperback)",
ISSN = "0269-3674",
LCCN = "QA297 .D85 1997",
bibdate = "Tue Jan 3 15:19:05 MST 2006",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
melvyl.cdlib.org:210/CDL90",
series = "Pitman Research Notes in Mathematics",
acknowledgement = ack-nhfb,
meetingname = "Dundee Conference on Numerical Analysis (17th: 1997)",
subject = "Numerical analysis; Congresses",
}
@Proceedings{Higham:2001:PEC,
editor = "Nicholas J. Higham and Roger Horn and Thomas J.
Laffey",
booktitle = "Proceedings of the {Eighth Conference of the
International Linear Algebra Society}",
title = "Proceedings of the {Eighth Conference of the
International Linear Algebra Society}",
publisher = pub-ELS,
address = pub-ELS:adr,
pages = "x--xii + 1--609",
year = "2001",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
MRclass = "00B25 (15-06)",
MRnumber = "MR1839422",
bibdate = "Sat Apr 16 17:55:00 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
note = "Held at the Universitat Politecnica de Catalunya,
Barcelona, July 19--22, 1999, Linear Algebra Appl. {\bf
332/334} (2001)",
acknowledgement = ack-nhfb,
}
@Proceedings{Brown:2007:PIS,
editor = "C. W. Brown",
booktitle = "{Proceedings of the 2007 International Symposium on
Symbolic and Algebraic Computation, July 29--August 1,
2007, University of Waterloo, Waterloo, Ontario,
Canada}",
title = "{Proceedings of the 2007 International Symposium on
Symbolic and Algebraic Computation, July 29--August 1,
2007, University of Waterloo, Waterloo, Ontario,
Canada}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "????",
year = "2007",
ISBN = "1-59593-743-9 (print), 1-59593-742-0 (CD-ROM)",
ISBN-13 = "978-1-59593-743-8 (print), 978-1-59593-742-1
(CD-ROM)",
LCCN = "QA76.5 S98 2007",
bibdate = "Fri Jun 20 08:53:37 2008",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/axiom.bib;
http://www.math.utah.edu/pub/tex/bib/issac.bib;
http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
note = "ACM order number 505070.",
acknowledgement = ack-nhfb,
}
@Book{Chan:2007:MMC,
editor = "Raymond H. Chan and Chen Greif and Dianne P. O'Leary",
booktitle = "Milestones in Matrix Computation: the Selected Works
of {Gene H. Golub} with Commentaries",
title = "Milestones in Matrix Computation: the Selected Works
of {Gene H. Golub} with Commentaries",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xi + 565 + 3",
year = "2007",
ISBN = "0-19-920681-3",
ISBN-13 = "978-0-19-920681-0",
LCCN = "QA188 .G67 2007",
MRclass = "65-06 (01A75 65Fxx)",
MRnumber = "MR2281939 (2008b:65004)",
MRreviewer = "David Scott Watkins",
bibdate = "Sat Apr 07 10:23:33 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
http://www.math.utah.edu/pub/tex/bib/numana2000.bib;
http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib;
http://www.math.utah.edu/pub/tex/bib/technometrics1970.bib",
URL = "http://www.loc.gov/catdir/enhancements/fy0737/2007276086-d.html",
abstract = "The text presents and discusses some of the most
influential papers in Matrix Computation authored by
Gene H. Golub, one of the founding fathers of the
field. The collection of 21 papers in divided into five
main areas: iterative methods for linear systems,
solution of least squares problems, matrix
factorizations and applications, orthogonal polynomials
and quadrature, and eigenvalue problems an commentaries
for each area are provided by leading experts: Anne
Greenbaum, {\AA}ke Bj{\"o}rck, Nicholas Higham, Walter
Gautschi, and G. W. (Pete) Stewart. Comments on each
paper are also provided by the original authors,
providing the reader with historical information on how
the paper came to be written and under what
circumstances the collaboration was undertaken.
Including a brief biography and facsimiles of the
original papers, this text will be of great interest to
students and researchers in numerical analysis and
scientific computation.",
acknowledgement = ack-nhfb,
tableofcontents = "List of Plates / x \\
I: Gene H. Golub \\
1 Gene H. Golub Biography, by Chen Greif / 3 \\
2 Publications of Gene H. Golub / 13 \\
3 Major Awards / 30 \\
4 Students of Gene H. Golub / 32 \\
II: Iterative Methods for Linear Systems \\
5 Commentary, by Anne Greenbaum / 35 \\
References / 43 \\
6 Chebyshev semi-iterative methods, successive
over-relaxation iterative methods, and second-order
Richardson iterative methods, Parts I and II (with R.
S. Varga) / 45 \\
7 A generalized conjugate gradient method for
non-symmetric systems of linear equations (with Paul
Concus) / 68 \\
8 A generalized conjugate gradient method for the
numerical solution of elliptic partial differential
equations (with Paul Concus and Dianne P. O'Leary) / 79
\\
9 Hermitian and Skew-Hermitian Splitting Methods for
Non-Hermitian Positive Definite Linear Systems (with
Zhong-Zhi Bai and Michael K. Ng) / 102 \\
III: Solution of Least Squares Problems \\
10 Commentary, by {\AA}ke Bj{\"o}rck / 129 \\
References / 141 \\
11 Numerical methods for solving linear least squares
problems / 148 \\
12 Singular value decomposition and least squares
solutions (with C. Reinsch) / 160 \\
13 The differentiation of pseudo-inverses and
non-linear least squares problems whose variables
separate (with V. Pereyra) / 181 \\
14 Generalized cross-validation as a method for
choosing a good ridge parameter (with M. Heath and G.
Wahba) / 202 \\
15 An analysis of the total least squares problem (with
C. Van Loan) / 213 \\
IV: Matrix Factorizations and Applications \\
16 Commentary, by Nicholas Higham / 227 \\
References / 233 \\
17 Calculating the singular values and pseudo-inverse
of a matrix (with W. Kahan) / 236 \\
18 The simplex method of linear programming using $ L U
$ decomposition (with R. H. Bartels) / 257 \\
19 On direct methods for solving Poisson's equation
(with B. L. Buzbee and C. W. Nielson) / 261 \\
20 Numerical methods for computing angles between
linear subspaces (with {\AA}. Bj{\"o}rck) / 292 \\
21 Methods for modifying matrix factorizations (with P.
E. Gill, W. Murray and M. A. Saunders) / 309 \\
V: Orthogonal Polynomials and Quadrature \\
22 Commentary, by Walter Gautschi / 345 \\
References / 354 \\
23 Calculation of Gauss quadrature rules (with J. H.
Welsch) / 359 \\
24 Matrices, moments, and quadrature (with G{\'e}rard
Meurant) / 380 \\
25 Computation of Gauss--Kronrod Quadrature Rules (with
D. Calvetti, W. B. Gragg and L. Reichel) / 434 \\
VI: Eigenvalue Problems \\
26 Commentary, by G. W. Stewart / 457 \\
References / 465 \\
27 Some modified matrix eigenvalue problems / 467 \\
28 Ill-conditioned eigensystems and the computation of
the Jordan canonical form (with J. H. Wilkinson) / 485
\\
29 The block Lanczos method for computing eigenvalues
(with R. Underwood) / 528 \\
30 The numerically stable reconstruction of a Jacobi
matrix from spectral data (with C. de Boor) / 546 Index
/ 563",
}
@Book{Hogben:2007:HLA,
editor = "Leslie Hogben",
booktitle = "Handbook of Linear Algebra",
title = "Handbook of Linear Algebra",
publisher = pub-CHAPMAN-HALL-CRC,
address = pub-CHAPMAN-HALL-CRC:adr,
pages = "xxx + 1370",
year = "2007",
ISBN = "1-58488-510-6 (hardcover), 1-4200-1057-3 (e-book)",
ISBN-13 = "978-1-58488-510-8 (hardcover), 978-1-4200-1057-2
(e-book)",
LCCN = "QA184.2 .H36 2007",
MRclass = "15-00 (00A20)",
MRnumber = "2279160 (2007j:15001)",
bibdate = "Fri Nov 21 06:49:56 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
http://www.math.utah.edu/pub/tex/bib/numana2000.bib;
z3950.loc.gov:7090/Voyager",
note = "Associate editors: Richard Brualdi, Anne Greenbaum and
Roy Mathias.",
series = "Discrete Mathematics and its Applications (Boca
Raton)",
URL = "http://www.crcnetbase.com/isbn/9781420010572;
http://www.crcnetbase.com/isbn/9781584885108;
http://www.loc.gov/catdir/enhancements/fy0647/2006045491-d.html",
abstract = "\booktitle{Handbook of Linear Algebra} covers all
aspects of linear algebra, including fundamentals,
numerical linear algebra, software packages for
computation in linear algebra, and various
applications, such as quantum computing, control
theory, image compression, and computational biology.
The author addresses combinatorial Matrix theory and
features Matrix notation throughout the text. The book
includes a chapter on software that provides extensive
coverage of MATLAB, Maple, and Mathematica and contains
details of Fortran subroutines available for linear
algebra such as LAPACK and ARPACK. Rather than
presenting long mathematical proofs, the text provides
numerous references for additional information.",
acknowledgement = ack-nhfb # " and " # ack-rah,
keywords = "Maple",
remark = "Associate editors: Richard Brualdi, Anne Greenbaum,
and Roy Mathias.",
subject = "Algebras, Linear",
tableofcontents = "Preliminaries \\
I. Linear algebra \\
1: Vectors, matrices and systems of linear equations /
Jane Day \\
2: Linear independence, span, and bases / Mark Mills
\\
3: Linear transformations / Francesco Barioli \\
4: Determinants and eigenvalues / Luz M. DeAlba \\
5: Inner product spaces, orthogonal projection, least
squares and singular value decomposition / Lixing Han
and Michael Neumann \\
6: Canonical forms / Leslie Hogben \\
7: Unitary similarity, normal matrices, and spectral
theory / Helene Shapiro \\
8: Hermitian and positive definite matrices / Wayne
Barrett \\
9: Nonnegative and stochastic matrices / Uriel G.
Rothblum \\
10: Partitioned matrices / Robert Reams \\
11: Functions of matrices / Nicholas J. Higham \\
12: Quadratic, bilinear and sesquilinear forms /
Raphael Lowey \\
13: Multilinear algebra / J. A. Dias de Silva and
Armando Machado \\
14: Matrix equalities and inequalities / Michael
Tsatsomeros \\
15: Matrix perturbation theory / Ren-Cang Li \\
16: Pseudospectra / Mark Embree \\
17: Singular values and singular value inequalities /
Roy Mathias \\
18: Numerical range / Chi-Kwong Li \\
19: Matrix stability and inertia / Daniel Hershkowitz
\\
20: Inverse eigenvalue problems / Alberto Borobia \\
21: Totally positive and totally negative matrices /
Shaun M. Fallat \\
22: Linear preserver problems / Peter \v Semrl \\
23: Matrices over integral domains / Shmuel Friedland
\\
24: Similarities of families of matrices / Shmuel
Friedland \\
25: Max-plus algebra / Marianne Akian, Ravindra Bapat,
St{\'e}phane Gaubert \\
26: Matrices leaving a cone invariant / Bit-Shun Tam
and Hans Schneider \\
II. Combinatorial matrix theory and graphs \\
27: Combinatorial matrix theory / Richard A. Brualdi
\\
28: Matrices and graphs / Willem H. Haemers \\
29: Digraphs and matrices / Jeffrey L. Stuart \\
30: Bipartite graphs and matrices / Bryan L. Shader \\
31: Permanents / Ian M. Wanless \\
32: D-optimal designs / Michael G. Neubauer and William
Watkins \\
33: Sign pattern matrices / Frank J. Hall and Zhongshan
Li \\
34: Multiplicity lists for the eigenvalues of symmetric
matrices with a given graph / Charles R. Johnson,
Ant{\'o}nio Leal Duarte, and Carlos M. Saiago \\
35: Matrix completion problems / Leslie Hogben and Amy
Wangsness \\
36: Algebraic connectivity / Steve Kirkland \\
III. Numerical methods \\
37: Vector and matrix norms, error analysis, efficiency
and stability / Ralph Byers and Biswa Nath Datta \\
38: Matrix factorizations, and direct solution of
linear systems / Christopher Beattie \\
39: Least squares solution of linear systems / Per
Christian Hansen and Hans Bruun Nielsen \\
40: Sparse matrix methods / Esmond G. Ng \\
41: Iterative solution methods for linear systems /
Anne Greenbaum \\
42: Symmetric matrix eigenvalue techniques / Ivan
Slapni\v car \\
43: Unsymmetric matrix eigenvalue techniques / David S.
Watkins \\
44: The implicitly restarted Arnoldi method / D. C.
Sorensen \\
45: Computation of the singular value decomposition /
Alan Kaylor Cline and Inderjit S. Dhillon \\
46: Computing eigenvalues and singular values to high
relative accuracy / Zlatko Drma{\v{c}} \\
47: Fast matrix multiplication / Dario A. Bini \\
48: Structured matrix computations / Michael Ng \\
49: Large-scale matrix computations / Roland W. Freund
\\
IV. Applications \\
50: Linear programming / Leonid S. Vaserstein \\
51: Semidefinite programming / Henry Wolkowicz \\
52: Random vectors and linear statistical models / Simo
Puntanen and George P. H. Styan \\
53: Multivariate statistical analysis / Simo Puntanen,
George A. F. Seber, and George P. H. Styan \\
54: Markov chains / Beatrice Meini \\
55: Differential equations and stability / Volker
Mehrmann and Tatjana Stykel \\
56: Dynamical systems and linear algebra / Fritz
Colonius and Wolfgang Kliemann \\
57: Control theory / Peter Benner \\
58: Fourier analysis / Kenneth Howell \\
59: Linear algebra and mathematical physics / Lorenzo
Sadun \\
60: Linear algebra in biomolecular modeling / Zhijun Wu
\\
61: Coding theory / Joachim Rosenthal and Paul Weiner
\\
62: Quantum computation / Zijian Diao \\
63: Information retrieval and web search / Amy
Langville and Carl Meyer \\
64: Signal processing / Michael Stewart \\
65: Geometry / Mark Hunacek \\
66: Some applications of matrices and graphs in
Euclidean geometry / Miroslav Fiedler \\
67: Matrix groups / Peter J. Cameron \\
68: Group representations / Randall Holmes and T. Y.
Tam \\
69: Nonassociative algebras / Murray R. Bremner, Lucia
I. Muakami and Ivan P. Shestakov \\
70: Lie algebras / Robert Wilson \\
V. Computational software \\
71: METLAB / Steven J. Leon \\
72: Linear algebra in Maple / David J. Jeffrey and
Robert M. Corless \\
73: Mathematica / Heikki Ruskeep{\"a}{\"a} \\
74: BLAS / Jack Dongarra, Victor Eijkhout, and Julien
Langou \\
75: LAPACK / Zhaojun Bai \\
76: Use of ARPACK and EIGS / D. C. Sorensen \\
77: Summary of Software for Linear Algebra Freely
Available on the Web / Jack Dongarra, Victor Eijkhout,
Julien Langou \\
G-1: Glossary \\
H-1: Notation Index",
}
@Book{Higham:2015:PCA,
editor = "Nicholas J. Higham and Mark R. Dennis and Paul
Glendinning and Paul A. Martin and Fadil Santosa and
Jared Tanner",
booktitle = "The {Princeton} Companion to Applied Mathematics",
title = "The {Princeton} Companion to Applied Mathematics",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xvii + 3 + 994 + 16",
year = "2015",
ISBN = "0-691-15039-7 (hardcover)",
ISBN-13 = "978-0-691-15039-0 (hardcover)",
LCCN = "QA155 .P75 2015",
bibdate = "Wed Sep 9 05:32:49 MDT 2015",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/subjects/companion-applied-mathematics.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://press.princeton.edu/titles/10592.html",
abstract = "This is the most authoritative and accessible
single-volume reference book on applied mathematics.
Featuring numerous entries by leading experts and
organized thematically, it introduces readers to
applied mathematics and its uses; explains key
concepts; describes important questions, laws, and
functions; looks at exciting areas of research; covers
modeling and simulation; explores areas of application;
and more. Modeled on the popular Princeton Companion to
Mathematics, this volume is an indispensable resource
for undergraduate and graduate students, researchers,
and practitioners in other disciplines seeking a
user-friendly reference book on applied mathematics.",
acknowledgement = ack-njh,
subject = "Algebra; Mathematics; Mathematical models",
tableofcontents = "Preface / ix \\
Contributors / xiii \\
Part I: Introduction to Applied Mathematics \\
I.1 What Is Applied Mathematics? / 1 \\
I.2 The Language of Applied Mathematics / 8 \\
I.3 Methods of Solution / 27 \\
I.4 Algorithms / 40 \\
I.5 Goals of Applied Mathematical Research / 48 \\
I.6 The History of Applied Mathematics / 55 \\
Part II: Concepts \\
II.1 Asymptotics / 81 \\
II.2 Boundary Layer / 82 \\
II.3 Chaos and Ergodicity / 82 \\
II.4 Complex Systems / 83 \\
II.5 Conformal Mapping / 84 \\
II.6 Conservation Laws / 86 \\
II.7 Control / 88 \\
II.8 Convexity / 89 \\
II.9 Dimensional Analysis and Scaling / 90 \\
II.10 The Fast Fourier Transform / 94 \\
II.11 Finite Differences / 95 \\
II.12 The Finite-Element Method / 96 \\
II.13 Floating-Point Arithmetic / 96 \\
II.14 Functions of Matrices / 97 \\
II.15 Function Spaces / 99 \\
II.16 Graph Theory / 101 \\
II.17 Homogenization / 103 \\
II.18 Hybrid Systems / 103 \\
II.19 Integral Transforms and Convolution / 104 \\
II.20 Interval Analysis / 105 \\
II.21 Invariants and Conservation Laws / 106 \\
II.22 The Jordan Canonical Form / 112 \\
II.23 Krylov Subspaces / 113 \\
II.24 The Level Set Method / 114 \\
II.25 Markov Chains / 116 \\
II.26 Model Reduction / 117 \\
II.27 Multiscale Modeling / 119 \\
II.28 Nonlinear Equations and Newton's Method / 120 \\
II.29 Orthogonal Polynomials / 122 \\
II.30 Shocks / 122 \\
II.31 Singularities / 124 \\
II.32 The Singular Value Decomposition / 126 \\
II.33 Tensors and Manifolds / 127 \\
II.34 Uncertainty Quantification / 131 \\
II.35 Variational Principle / 134 \\
II.36 Wave Phenomena / 134 \\
Part III: Equations, Laws, and Functions of Applied
Mathematics \\
III.1 Benford's Law / 135 \\
III.2 Bessel Functions / 137 \\
III.3 The Black--Scholes Equation / 137 \\
III.4 The Burgers Equation / 138 \\
III.5 The Cahn--Hilliard Equation / 138 \\
III.6 The Cauchy--Riemann Equations / 139 \\
III.7 The Delta Function and Generalized Functions /
139 \\
III.8 The Diffusion Equation / 142 \\
III.9 The Dirac Equation / 142 \\
III.10 Einstein's Field Equations / 144 \\
III.11 The Euler Equations / 146 \\
III.12 The Euler--Lagrange Equations / 147 \\
III.13 The Gamma Function / 148 \\
III.14 The Ginzburg--Landau Equation / 148 \\
III.15 Hooke's Law / 149 \\
III.16 The Korteweg--de Vries Equation / 150 \\
III.17 The Lambert $W$ Function / 151 \\
III.18 Laplace's Equation / 155 \\
III.19 The Logistic Equation / 156 \\
III.20 The Lorenz Equations / 158 \\
III.21 Mathieu Functions / 159 \\
III.22 Maxwell's Equations / 160 \\
III.23 The Navier--Stokes Equations / 162 \\
III.24 The Painlev{\'e} Equations / 163 \\
III.25 The Riccati Equation / 165 \\
III.26 Schr{\"o}dinger's Equation / 167 \\
III.27 The Shallow-Water Equations / 167 \\
III.28 The Sylvester and Lyapunov Equations / 168 \\
III.29 The Thin-Film Equation / 169 \\
III.30 The Tricomi Equation / 170 \\
III.31 The Wave Equation / 171 \\
Part IV: Areas of Applied Mathematics \\
IV.1 Complex Analysis / 173 \\
IV.2 Ordinary Differential Equations / 181 \\
IV.3 Partial Differential Equations / 190 \\
IV.4 Integral Equations / 200 \\
IV.5 Perturbation Theory and Asymptotics / 208 \\
IV.6 Calculus of Variations / 218 \\
IV.7 Special Functions / 227 \\
IV.8 Spectral Theory / 236 \\
IV.9 Approximation Theory / 248 \\
IV.10 Numerical Linear Algebra and Matrix Analysis /
263 \\
IV.11 Continuous Optimization (Nonlinear and Linear
Programming) / 281 \\
IV.12 Numerical Solution of Ordinary Differential
Equations / 293 \\
IV.13 Numerical Solution of Partial Differential
Equations / 306 \\
IV.14 Applications of Stochastic Analysis / 319 \\
IV.15 Inverse Problems / 327 \\
IV.16 Computational Science / 335 \\
IV.17 Data Mining and Analysis / 350 \\
IV.18 Network Analysis / 360 \\
IV.19 Classical Mechanics / 374 \\
IV.20 Dynamical Systems / 383 \\
IV.21 Bifurcation Theory / 393 \\
IV.22 Symmetry in Applied Mathematics / 402 \\
IV.23 Quantum Mechanics / 411 \\
IV.24 Random-Matrix Theory / 419 \\
IV.25 Kinetic Theory / 428 \\
IV.26 Continuum Mechanics / 446 \\
IV.27 Pattern Formation / 458 \\
IV.28 Fluid Dynamics / 467 \\
IV.29 Magnetohydrodynamics / 476 \\
IV.30 Earth System Dynamics / 485 \\
IV.31 Effective Medium Theories / 500 \\
IV.32 Mechanics of Solids / 505 \\
IV.33 Soft Matter / 516 \\
IV.34 Control Theory / 523 \\
IV.35 Signal Processing / 533 \\
IV.36 Information Theory / 545 \\
IV.37 Applied Combinatorics and Graph Theory / 552 \\
IV.38 Combinatorial Optimization / 564 \\
IV.39 Algebraic Geometry / 570 \\
IV.40 General Relativity and Cosmology / 579 \\
Part V: Modeling \\
V.1 The Mathematics of Adaptation (Or the Ten Avatars
of Vishnu) / 591 \\
V.2 Sport / 598 \\
V.3 Inerters / 604 \\
V.4 Mathematical Biomechanics / 609 \\
V.5 Mathematical Physiology / 616 \\
V.6 Cardiac Modeling / 623 \\
V.7 Chemical Reactions / 627 \\
V.8 Divergent Series: Taming the Tails / 634 \\
V.9 Financial Mathematics / 640 \\
V.10 Portfolio Theory / 648 \\
V.11 Bayesian Inference in Applied Mathematics / 658
\\
V.12 A Symmetric Framework with Many Applications / 661
\\
V.13 Granular Flows / 665 \\
V.14 Modern Optics / 673 \\
V.15 Numerical Relativity / 680 \\
V.16 The Spread of Infectious Diseases / 687 \\
V.17 The Mathematics of Sea Ice / 694 \\
V.18 Numerical Weather Prediction / 705 \\
V.19 Tsunami Modeling / 712 \\
V.20 Shock Waves / 720 \\
V.21 Turbulence / 724 \\
Part VI: Example Problems \\
VI.1 Cloaking / 733 \\
VI.2 Bubbles / 735 \\
VI.3 Foams / 737 \\
VI.4 Inverted Pendulums / 741 \\
VI.5 Insect Flight / 743 \\
VI.6 The Flight of a Golf Ball / 746 \\
VI.7 Automatic Differentiation / 749 \\
VI.8 Knotting and Linking of Macromolecules / 752 \\
VI.9 Ranking Web Pages / 755 \\
VI.10 Searching a Graph / 757 \\
VI.11 Evaluating Elementary Functions / 759 \\
VI.12 Random Number Generation / 761 \\
VI.13 Optimal Sensor Location in the Control of
Energy-Efficient Buildings / 763 \\
VI.14 Robotics / 767 \\
VI.15 Slipping, Sliding, Rattling, and Impact:
Nonsmooth Dynamics and Its Applications / 769 \\
VI.16 From the $N$-Body Problem to Astronomy and Dark
Matter / 771 \\
VI.17 The $N$-Body Problem and the Fast Multipole
Method / 775 \\
VI.18 The Traveling Salesman Problem / 778 \\
Part VII: Application Areas \\
VII.1 Aircraft Noise / 783 \\
VII.2 A Hybrid Symbolic--Numeric Approach to Geometry
Processing and Modeling / 787 \\
VII.3 Computer-Aided Proofs via Interval Analysis / 790
\\
VII.4 Applications of Max-Plus Algebra / 795 \\
VII.5 Evolving Social Networks, Attitudes, and Beliefs
--- and Counterterrorism / 800 \\
VII.6 Chip Design / 804 \\
VII.7 Color Spaces and Digital Imaging / 808 \\
VII.8 Mathematical Image Processing / 813 \\
VII.9 Medical Imaging / 816 \\
VII.10 Compressed Sensing / 823 \\
VII.11 Programming Languages: An Applied Mathematics
View / 828 \\
VII.12 High-Performance Computing / 839 \\
VII.13 Visualization / 843 \\
VII.14 Electronic Structure Calculations (Solid State
Physics) / 847 \\
VII.15 Flame Propagation / 852 \\
VII.16 Imaging the Earth Using Green's Theorem / 857
\\
VII.17 Radar Imaging / 860 \\
VII.18 Modeling a Pregnancy Testing Kit / 864 \\
VII.19 Airport Baggage Screening with X-Ray Tomography
/ 866 \\
VII.20 Mathematical Economics / 868 \\
VII.21 Mathematical Neuroscience / 873 \\
VII.22 Systems Biology / 879 \\
VII.23 Communication Networks / 883 \\
VII.24 Text Mining / 887 \\
VII.25 Voting Systems / 891 \\
Part VIII: Final Perspectives \\
VIII.1 Mathematical Writing / 897 \\
VIII.2 How to Read and Understand a Paper / 903 \\
VIII.3 How to Write a General Interest Mathematics Book
/ 906 \\
VIII.4 Workflow / 912 \\
VIII.5 Reproducible Research in the Mathematical
Sciences / 916 \\
VIII.6 Experimental Applied Mathematics / 925 \\
VIII.7 Teaching Applied Mathematics / 933 \\
VIII.8 Mediated Mathematics: Representations of
Mathematics in Popular Culture and Why These Matter /
943 \\
VIII.9 Mathematics and Policy / 953 \\
Index / 963",
}
@Proceedings{Burgess:2017:ISC,
editor = "Neil Burgess and Javier Bruguera and Florent de
Dinechin",
booktitle = "{24th IEEE Symposium on Computer Arithmetic (ARITH
24), London, UK, 24--26 July 2017}",
title = "{2017 IEEE 24th Symposium on Computer Arithmetic
(ARITH 24), London, UK, 24--26 July 2017}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 198",
year = "2017",
ISBN = "1-5386-1966-0 (print), 1-5386-1965-2, 1-5386-1964-4",
ISBN-13 = "978-1-5386-1966-7 (print), 978-1-5386-1965-0,
978-1-5386-1964-3",
ISSN = "1063-6889",
LCCN = "QA76.9.C62 S95 2017",
bibdate = "Fri Nov 17 10:14:11 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/gnu.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=8019911",
acknowledgement = ack-nhfb,
keywords = "computer arithmetic units; correctness proofs;
cryptography; domain specific designs; error analysis;
exascale computing; floating point arithmetic;
floating-point error analysis; formal verification;
function approximation; modular arithmetic; theorem
proving; verification",
}
@Article{Sukkari:2019:QBS,
author = "Dalal Sukkari and Hatem Ltaief and Aniello Esposito
and David Keyes",
title = "A {QDWH}-based {SVD} Software Framework on
Distributed-memory Manycore Systems",
journal = j-TOMS,
volume = "45",
number = "2",
pages = "18:1--18:21",
month = apr,
year = "2019",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3309548",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon May 6 18:23:42 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See \cite{Nakatsukasa:2013:SES}.",
URL = "https://dl.acm.org/citation.cfm?id=3309548",
abstract = "This article presents a high-performance software
framework for computing a dense SVD on
distributed-memory manycore systems. Originally
introduced by Nakatsukasa et al. (2010) and Nakatsukasa
and Higham (2013), the SVD solver relies on the polar
decomposition using the QR Dynamically Weighted Halley
algorithm (QDWH). Although the QDWH-based SVD algorithm
performs a significant amount of extra floating-point
operations compared to the traditional SVD with the
one-stage bidiagonal reduction, the inherent high level
of concurrency associated with Level 3 BLAS
compute-bound kernels ultimately compensates for the
arithmetic complexity overhead. Using the ScaLAPACK
two-dimensional block cyclic data distribution with a
rectangular processor topology, the resulting QDWH-SVD
further reduces excessive communications during the
panel factorization, while increasing the degree of
parallelism during the update of the trailing
submatrix, as opposed to relying on the default square
processor grid. After detailing the algorithmic
complexity and the memory footprint of the algorithm,
we conduct a thorough performance analysis and study
the impact of the grid topology on the performance by
looking at the communication and computation profiling
trade-offs. We report performance results against
state-of-the-art existing QDWH software implementations
(e.g., Elemental) and their SVD extensions on
large-scale distributed-memory manycore systems based
on commodity Intel x86 Haswell processors and Knights
Landing (KNL) architecture. The QDWH-SVD framework
achieves up to 3/8-fold speedups on the
Haswell/KNL-based platforms, respectively, against
ScaLAPACK PDGESVD and turns out to be a competitive
alternative for well- and ill-conditioned matrices. We
finally come up herein with a performance model based
on these empirical results. Our QDWH-based polar
decomposition and its SVD extension are freely
available at https://github.com/ecrc/qdwh.git and
https://github.com/ecrc/ksvd.git, respectively, and
have been integrated into the Cray Scientific numerical
library LibSci v17.11.1.",
acknowledgement = ack-nhfb,
articleno = "18",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
