A Complete Bibliography of Publications of Beresford N. Parlett

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: beebe@math.utah.edu, beebe@acm.org,
                  beebe@computer.org (Internet)
      WWW URL: http://www.math.utah.edu/~beebe/

10 February 2022 Version 1.63

Abstract This bibliography records publications of Beresford N. Parlett.

Title word cross-reference

(A − λM)x = 0 [NNOP86]. (K − λM)z = 0 [Par80a, Par81d]. 2 [PH91, PH92, PH94]. $24.80 [Par79]. 3 [ZPP05a, ZPP05b]. AX = b [Par81c]. dqds [PM00, PM02]. Eig3 [For64]. exp(Bt) [PN85]. K [Par80a, Par81d]. LDL^{t} [Par00b]. LR [FP09, GP11, Par64a]. LU [Par67a, PP73]. M [Par80a, Par81d]. N × N [Par69]. Eig [Var66]. QL [PH78]. QR [LP88, Par65a, Par67a, Par67d, PK69, PL93, Par00a, Par66d, PP73]. T [Par00b]. φ [Koi09].

-functions [Koi09].

16th [Par79]. 1968 [Mor69]. 1972 [Gre72]. 1975 [BR76]. 1981 [GL82]. 1985 [GL86]. 1987 [GGMP88]. 1990 [Alb91]. 1992 [MGD93, RRV93]. 1993 [BCEP94]. 1995 [Ise95]. 19th [Par79].

205 [NNOP86, PNON84]. 25-March [Alb91]. 26 [HP92b]. 2e [Abs80]. 2nd [Abs80].

517 [CFP77].

68077a [HP92b]. 68077b [HP92b].

880 [MVDP09]. 89 [KvSR90]. 894 [Koi09].

94e [HP92b].

= [Abs80, Alb91].

Accuracy [DMPV07a, Par66b, DMPV08, Par05]. Accurate [BP00, FP92a, FP92b, FP93a, FP94, MNP83, MNP84, PN86, BPV00, BP03, BPV06, PN85]. Acta [Ise95]. Advanced [MGD93]. ahead [PT81b, PTL84, PTL85]. Algebra [Lew94, MGD93, WR71, RRV93, SP09, Par72b]. Algebraic [Par66a]. ALGOL [For64, Var66]. Algorithm [DPV04, DPV05, LGP14, MPV05, Par64b, Par68, PH78, PS79, PR81, PSS82, Par90b, Par94, Par00a, Par02b, PV04, SS17, BEK97, DH03, DPV06, FP09, FP22, HP77, HP78, Koi09, MPV06, Par65a, Par66c, PK69, PS77, Par80b, PT81b, PNO82a, Par82a, PTL84, PN85, PTL85, Par87b, PC90a, PM00, PM02, RBS66, CFP77, Koi09, MVDP09, Par67d]. Algorithms [CW85, FP92a, KP74, Par71, PNOJ85, BOW77, FP92b, FP93a, FP93b, FP93c, FP94, FP95, GP11, Par67a, Par95]. allow [LP08]. Amer [HP92b]. Among [Par76a, PNOL88, Par92b]. AMS [RSS96]. Analysis [KP74, Par71, Par74c, Par78, Par90a, SS17, BOW77, GP90, NN94, Par77c, Par79, Par81b, Par87a, RSS96, SCI^{+}96, WG96]. Analytic [Par81c]. anyone [Par67b]. Application [PD97]. Applications [MGD93, Par62, Num85, SP86, Par74a]. Applied [GL84, Lew94, Par64c, RSS96, GL82, GL86]. approaches [PH96]. Approximate [KPJ82, PPV93, PPv95]. Approximation [BIP97]. Argonne [BR76]. art [Par87c]. Assigned [KPRV97]. augmented [BPW05]. August [MGD93, Mor69, RSS96]. automated [Ard80]. Automatic [Par72b].

B [HP92b, Par81a]. backward [WW20]. Balancing [PR69]. Based [Par92c, TW92, HP92b, Koi09, Par89]. Basic [Par68, Par92c, HP92b, Par89]. be [Ard80, Par72a]. Behandlung [Alb91]. Belgium [MGD93]. Beresford [Bun95]. Berlin [Par79]. bidiagonal [Par05]. bidiagonals [Par97, Par98a]. Bisectors [Par71]. black [PNO89]. Block [PS87b, SP86, SP88, Koi09]. blocks [Par77b, PN87]. Book [Par66a, Par74a, Par74c, Par79, PT81a, Par81a, Par10, Par72b]. Bound [PNO85, PNO83]. Bounds [KPJ82, PPV93, PPv95]. box [PNO89]. Budde [Par64b]. Bull [HP92b]. Bunch [Par81a]. Bundles [Par62].

C [Par81a, Par72b]. CA [BBG^{+}95]. calcul [Par73a]. calculation [PR69, Par73a]. calculations [PH91, PH92, PH94]. Calculator [KP77, KP78b]. Can [KP77, KP78b, Par72a, PV04, Ard80]. Canonical [Par67c]. Carolina [BCEP94]. case [PM00, PM02]. Centenary [BCEP94]. Center [Gre72]. century [Par79]. Certification [Var66]. Chaussées [GGMP88]. Chislennye [Par83a]. choice [NNOP86]. Cholesky [EM95, FP93c, FP95, GP88, GP90]. Circle [Par09a]. circulants [Par82b]. City [RSS96]. Classical [SS17]. Cliffs [Par74c]. clustered [Par96a]. Clusters [PV04, Par96c]. cm. [Par74c]. Communication [GP88, GP90]. Comparison [NOPR88, PNOR87]. Compiler [PW75, PW77]. complementary [Par09a]. Complex [PS85, PS87a]. Complexity [Par92c, TW92, HP92b, Par81c, Par89]. Computation [GOP^{+}79, GOP^{+}80, MNP84, Par74d, Par72b, RRV93, SP86, SP88, CH90, MNP83, PN86, PS87b, RGO^{+}79, SCI^{+}96, Par09b]. computational [BOW77]. Computations [BR76, CW85, MPV05, MPV06]. compute [CFP75, DP04a, PF75]. computer [Ard80]. Computers [PNOJ85, RW67]. Computing [BBG^{+}95, BPS94, CFP77, GL82, GL84, GL86, Nas90, CFP75, DH03, NN94, PNON84, PC88, PC90b, RBS66, GL82, GL86]. Condition [CFP77, CFP75]. conducted [Gre72]. Conference [BBG^{+}95, BCEP94, Lew94, RRV93]. Congrès [Abs80]. Congress [Abs80, Mor69]. Conjugate [NOPR88, LP08, PNOR87]. Construction [KPRV97, Par96c]. Contribution [Par90a, Par87a]. converge [PL91]. Convergence [FP09, Par65a, Par66c, Par68, PH78, BP66, HP77, HP78, PK69, Par67d]. Cornelius [BCEP94]. Correction [Par67d]. COSERS [Ard80]. Cost [PW75, GP88, PW77]. Count [KP77, KP78b]. CYBER [NNOP86, PNON84].

D [BIP97, PH91, PH92, PH94, ZPP05a, ZPP05b]. damped [PC88, PC90b]. dans [Abs80]. December [BCEP94, GL82, GL84, GL86]. Decomposition [BKP76, GGMP88, Par67c, EM95]. Dedicated [Bun95]. Dedication [GP91]. Definite [PR70, PKS02]. deflation [PS77]. Design [DPV04, DPV06]. designed [Par08]. Detecting [VP11]. determinant [Par02a]. determines [Par05]. Development [Par64a, PN85]. Diagonal [BPP81, Par77b, PN87, Par03b]. diameter [Par03b]. difference [Par66b]. Differences [MNP84, MNP83]. Differential [FP92a, FP93b, GGMP88, FP92b, FP93a, FP94, PF94a, PF94b, PF95]. Digital [RW67]. Direct [BP71]. directions [RGO^{+}79]. discovered [GP11]. Discriminant [ZPP05a, Par02a]. discussion [PK69, SCI^{+}96]. dissipation [Par66b]. Divided [MNP84, MNP83]. Do [Par94]. Does [SCI^{+}96]. Domain [GGMP88]. Donald [Par74a]. Dongarra [Par81a]. Double [PD97]. Doubly [PL82, PL81]. dqds [FP22, LGP14]. dynamics [Gre72].

Ecole [GGMP88]. ed [Par74a]. Edinburgh [Mor69]. Editor [Par67e]. Editorial [Bun95]. Editors [HP92b]. Effect [NNOP86, PNON84]. Efroymson [PT81a]. eigenpair [MPV06]. Eigenpairs [FP20, Par03a]. Eigenproblems [PR81, PTL84]. Eigensolvers [DMPV07a, DMPV07b, DMPV08, MVDP09]. Eigensystems [KPJ82]. Eigenvalue [BP00, CW85, For64, Par64c, Par65b, Par66a, Par80c, PT81a, PSS82, Par98b, PKS02, PV04, Var66, Alb91, BPV00, BP03, BPV06, FP22, NNOP86, NOPT80, NOPT83a, PPV93, PPv95, Par62, Par83a, PL92, Par10]. Eigenvalues [CFP77, Par67b, Par84, PNO85, CFP75, FPD12, Par67e, PR69, Par73a, PNO82a, Par83b, PNO83, Par87c, Par96a]. Eigenvector [PWW83, PW84, PDF16]. Eigenvectors [CFP77, DP02, DP03, DP04b, CFP75, DP04a, PR69, Par87c, Par96c, Par96b]. Eigenwertaufgaben [Alb91]. Element [NOP85, NOPR88, PNO82b, BOW77, LNOP82, NOPT83b, Par76b, Par77a, PNOL81, PNOR87]. Elements [Par76a]. Engineering [GL84, Abs80, Ard80, GL82, GL86]. Englewood [Par74c]. enlighten [Par08]. entertain [Par08]. entries [Par03b]. equation [FPD95]. Equations [BP71, GGMP88, MMP11, PR70, Par74a, NOPT83b, Par80b]. Ergodic [Par70]. Error [PNO85, Par76b, Par77a, PNO83, WW20]. estimate [Koi09]. Estimating [PSS82]. Explicit [KPRV97]. Exponential [MNP84, MNP83, PN86]. extracting [Par87c]. Extraction [Par84, Par83b]. Extremal [BPS94].

F [HP92b]. F2 [CFP77]. factored [Par03a]. Factorization [PW75, PD97, ZPP05a, GP88, GP90, PW77]. Fail [PV04]. failure [PL91]. far [KP76, KP78a]. Fast [LNOP82, PNOL81]. Februar [Alb91]. February [Alb91, BBG^{+}95]. Federation [Mor69]. Fernando [PD97]. Fields [ZPP05a, ZPP05b]. Fifth [GL82, Lew94]. Fill [LNOP82, PNOL81]. Fill-in [LNOP82, PNOL81]. find [FPD95]. finding [Par67e]. Finite [LNOP82, BOW77, NOPT83b, Par76b, Par77a, PNOL81]. Finite-element [LNOP82]. First [GGMP88, GGMP88]. Form [PF75, PL82, Par92a, Par69, PL81, Par90c]. Formulations [BOW77]. Forward [PL93, LP88, PL91]. Fourier [Par82b]. France [GL82, GL84, GL86, GGMP88]. Francisco [BBG^{+}95]. Free [LNOP82, PNOL81]. French [Par73a]. frequencies [PNON84]. Frequency [PH96]. Fully [Par94]. Function [MNP84, MNP83, Par72a, Par03b]. Functions [Par74d, Par76a, Par09b, BEK97, DH03, Koi09]. Future [GOP^{+}79, GOP^{+}80].

G [PT81a, Par81a]. Gaps [DP02, DP03, DP04b]. general [Par10]. Generalizations [Par74b]. generalized [BPW05, RBS66]. Geometric [PP73, Par73a]. géométrique [Par73a]. German [KP78b]. Germany [BOW77]. Gersgorin [Par09a]. Givens [GP91]. Global [Par68, PH78, HP77, HP78]. globally [WW20]. Glued [DPV05, PV09]. go [KP76, KP78a]. Goldstine [Par79]. GR [Par10]. Gradient [NOPR88, LP08, PNOR87]. Gram [Par96b]. growing [PNO82a]. Guide [Par81a].

H [HP92b, Par66a, Par74c, Par79, Par87a, Par90a, Par72b]. H. [Par74c]. Hadamard [Par96d, Par07]. Hall [Par74c]. Handbook [Par72b]. Heidelberg [Par79]. Herman [Par79]. Hertelendy [Par74c]. Hessenberg [Par66c, Par67c, Par68, Par73b]. Hessian [ZPP05a]. Higham [Par09b]. History [Nas90, Par79]. hyperbolic [Par05]. hypercube [GP88, GP90]. Hyperdominant [KPRV97].

IFIP [Mor69]. Ihren [KP78b]. II [Par72b, Par62]. Implement [NOPEJ87, NOP84]. Implementation [DPV04, PNOJ85, PH91, DPV06, PM00, PM02]. Implicit [FP93c, FP95, PS77]. Improved [LGP14]. Indefinite [BP71, PC88, PC90a, PC90b]. independence [Par62]. Independent [MMP11]. inequality [EM95]. Influence [PW75, PW77]. Information [Mor69, Par92c, TW92, HP92b, Par89, Mor69]. Information-Based [Par92c, TW92, HP92b, Par89]. Infrastructure [DMPV07b, MVDP09]. ingénieur [Abs80]. inner [PC88, PC90a]. Instability [PL93, LP88, PL91]. Institute [MGD93]. Interlacing [HP92a, HP91]. International [Abs80, BP00, BCEP94, GL82, GL84, GL86, GGMP88, KvSR90, Mor69, Abs80]. Invariant [Par66d, Par96a, VP11, WW20]. Inverse [PDF16, Koi09, RBS66]. Invert [PS87a, PS85]. Ising [PH91, PH92, PH94]. issue [BP03, BPV06]. Iteration [Par74b, NOPT80, NOPT83a]. Iterations [PP73, LP08].

J [BIP97, HP92b, Par66a, Par74a, Par74c, Par81a, Par09b, Par72b]. J. [GP91, Par87a, Par90a]. January [GGMP88]. Jiang [WW20]. July [RSS96]. June [Gre72, Lew94].

Kahan [Bun95, WW20]. Kent [RRV93]. Können [KP78b]. Kostant [SP09]. Krylov [Par10, PPV93, PPv95].

Laboratory [BR76]. Laguerre [Par62, Par64c]. Lanczos [BCEP94, CW85, KP74, KP76, KP78a, NOPT80, NOPT83a, NOPT83b, NOPR88, PS77, Par80b, PT81b, PR81, Par82a, PNOJ85, PNOR87, Par87b, PNOL88, PNO89, PC90a, Par90b, Par92b, Par94, PS79, PSS82, PTL84, PTL85]. LAPACK [DMPV07a, DDP^{+}07, DMPV07b, DMPV08]. Large [CW85, MGD93, PR81, Par80a, Par81d, PTL84, Par74a]. Largest [PSS82, PKS02]. Letter [Par67e]. Leuven [MGD93]. Libraries [DDP^{+}07]. Lie [SP09]. Linear [BP71, Lew94, MMP11, PR70, Par74a, Par72b, SP09, WR71, BPW05, Par62, Par80b, RRV93, MGD93]. Lines [ZPP05a]. LINPACK [Par81a]. Localization [VP11]. look [Par80b, PT81b, PTL84, PTL85]. look-ahead [PT81b, PTL85].

M. [BIP97]. Madison [Gre72]. maintain [PNOL88]. maintaining [Par92b]. March [Alb91, RRV93]. marriage [Par72a]. März [Alb91]. Math [HP92b]. Mathematical [PW75, RW67, PW77]. Mathematics [Gre72, Par79, RSS96]. Matrices [BPS94, DPV05, FP20, KP74, KPJ82, KPRV97, Par66d, Par67c, Par68, Par74a, Par74d, Par74b, Par76a, Par84, PS87a, PS08, Par09b, PDF16, BEK97, DP04a, FP95, LP08, Par62, Par66c, Par67e, Par69, Par73b, PT81b, PWW83, Par83b, PW84, PS85, PTL85, Par03a, Par74c]. Matrix [BKP76, BR76, CFP77, NN94, Par64c, Par65b, PR70, PT81a, PKS02, SS17, BPP81, BP66, CFP75, DH03, DP10, EM95, FP09, FPD12, Par62, PR69, PF75, PNO82a, PN86, Par91, Par02a, Par05, PB06, PV09, Par10, RBS66]. mechanics [Par87c]. meets [SP09]. Memory [BPS94]. Method [Par64c, NNOP86, NOPT83b, Par62, PH92, PH94]. méthodes [Par73a, Abs80]. Methods [BP71, GL84, GGMP88, Par64a, PL81, PL82, RW67, Abs80, BPW05, GL82, GL86, Par73a, Par83a, PNON84, Par10, Par10]. metody [Par83a]. Minimal [Par92a, Par90c, PH91, PH92, PH94, PH97]. Minimum [PL92]. minors [Par62]. Misconvergence [Par87b, Par90b]. missed [Par96d, Par07]. model [Par70, PH91, PH92, PH94, SCI^{+}96]. modes [PC88, PC90b]. Moler [Par81a]. moment [Par73b]. monitoring [Par82a]. most [FPD95]. MR1102755 [HP92b]. MR1102756 [HP92b]. MR2164298 [Par10]. MR2383888 [Par10]. MRRR [DPV04, DPV05, DPV06, MPV05, MPV06, PV04]. MTNS [KvSR90]. MTNS-89 [KvSR90]. Multiple [DP04a]. multiplications [Par69]. Multiprocessor [BPS94].

N [HP92b, Par74c]. N.S [HP92b]. National [BR76]. Nationale [GGMP88]. NATO [MGD93]. natural [PNON84, PC88, PC90b]. nature [RGO^{+}79]. Nearly [PH97]. need [SCI^{+}96]. Newton [NOPT83b]. Next [DDP^{+}07]. Nicholas [Par09b]. no [HP92b]. nonlinear [NOPT83b]. Nonnormal [KPJ82, Par74b]. nonsymmetric [FP22, LP08]. norm [EM95]. Normal [Par73b]. North [BCEP94]. Note [Par64b, GP90]. Notes [For64, Par64b, Par66d, Par67c, Par69, Var66]. number [Par69]. Numbers [CFP77, CFP75]. Numerica [Ise95]. Numerical [Abs80, GOP^{+}79, GOP^{+}80, Par78, Par83a, Par90a, RRV93, RGO^{+}79, WG96, CH90, Par77c, Par79, Par81b, Par87a, RSS96, SCI^{+}96, Alb91, Par74c, Par10, RRV93]. numériques [Abs80]. Numerische [Alb91].

Oberwolfach [Alb91]. Ohio [RRV93]. one [FP09, Par70]. one-point [FP09]. optimal [WW20]. optimization [BIP97]. Order [MMP11, PH97]. organized [Mor69]. Orthogonal [DP02, DP03, DP04b, Par96b, BPP81, DP04a, Par96c, PB06]. orthogonality [PNOL88, Par92b]. Orthogonalization [PS79]. overrelaxation [BPW05].

P [Par74c]. PA [Par09b]. Panel [SCI^{+}96]. Papers [For64, Par64b, Par66d, Par67c, Var66]. Parallel [BBG^{+}95, PF94a, GP90, NN94]. parallelization [BEK97]. Paris [GGMP88]. Park [RSS96]. Parlett [HP92b, WW20, BEK97, Bun95, DH03, EM95, For64, Koi09, Var66]. Partial [GGMP88]. Particular [PW75, PW77]. Past [GOP^{+}79, GOP^{+}80]. pencils [PC90b, Par91]. Performance [DMPV07a, DMPV08]. Perspectives [HP92b, TW92]. Perturbation [Par03a, WW20]. Philadelphia [Par09b]. Physical [Par79]. plots [PH96]. point [FP09, LP08]. Ponts [GGMP88]. Population [Gre72]. populations [Par70]. Positive [PKS02, PM00, PM02]. Powell [BIP97]. Power [PP73]. powers [BP66]. pp [Par74c, Par79, Par09b]. practical [PK69]. Preconditioning [NOPR88, SS17, NOP85, PNO82b, PNOR87]. Preface [BPV06]. Prentice [Par74c]. Prentice-Hall [Par74c]. prescribed [PS08]. Present [GOP^{+}79, GOP^{+}80]. Présentation [Par73a, Par73a]. Problem [Par64c, Par80c, PD97, Par98b, PDF16, FP22, NNOP86, Par62, Par83a, Par10, Par66a, PT81a]. problema [Par83a]. Problems [LNOP82, Par65b, Par00c, Alb91, BPV00, BP03, BPV06, NOPT80, NOPT83a, PNOL81, BP00, Par00c, Par10]. Procedure [For64, Var66]. Proceedings [BR76, GL84, GGMP88, Lew94, MGD93, GL82, GL86, Gre72, Mor69, RRV93, BBG^{+}95, BP00, BCEP94, KvSR90]. process [KP76, KP78a]. Processing [BBG^{+}95, Mor69]. product [Par69, PC88, PC90a]. products [Par97, Par98a]. Program [CFP77, CFP75, PF75, Par77b, PNO89]. Programs [PN87]. Progress [Par77c, Par78, Par81b, PR81]. Proof [PH78, HP77, HP78]. Properties [HP92a, HP91, Par70]. propres [Par73a]. Prospectus [DDP^{+}07].

Q [Par66c]. Q-R [Par66c]. qd [FP92a, FP92b, FP93a, FP93b, FP94, GP11, PF94a, PF94b, PF95, Par97, Par95]. QL [HP77, HP78]. QR [Par68, PL91, Par02b]. Quotient [Par74b].

R [Par74c, Par81a, Par66c]. Raleigh [BCEP94]. Ralph [Par74a]. Rayleigh [Par74b]. Real [MGD93, PS87a, PDF16, FP22, Par67e, PF75, PS85]. Real-Time [MGD93]. Realizations [Par92a, Par90c]. Rechner [KP78b]. Recollections [Par08]. Recurrence [Par76a]. reduced [PH97]. Reduction [Par90c, Par92a]. redundant [FPD95]. Refined [HP91, HP92a, PNO85, PNO83]. Reflections [Par71]. Reflectors [SP88, PS87b, SP86]. Reid [Par74a]. Reinsch [Par72b]. Relative [DP02, DP03, DP04b, Par05]. Relatively [PD00]. Reliable [CH90]. remarks [HP92b]. replace [Par00b]. Report [GOP^{+}79, GOP^{+}80]. representation [PH91]. Representations [PD00, DP04a, PH92, PH94]. required [Par69]. Research [GOP^{+}79, GOP^{+}80, Gre72, Ard80, RGO^{+}79]. Residual [KPJ82]. response [PH96]. result [Par09a]. Revelations [DP10]. Review [Par66a, Par74a, Par74c, Par79, PT81a, Par81a, Par09b, Par10, Par72b]. rewards [Par92b]. Ritz [PS08]. Robust [PD00]. Rose [Par74a]. Roundoff [Par76b, Par77a]. Russian [Par83a]. Rutishauser [Par74c].

S [PT81a]. saddle [LP08]. San [BBG^{+}95]. ScaLAPACK [DDP^{+}07]. Scale [MGD93]. Scaling [PL82, BPP81, PL81]. Scene [Par84, Par83b]. schemes [Par66b, Par82a]. Schmidt [Par96b]. Schur [DH03, Koi09, PF75]. Schwarz [Par74c]. science [Ard80]. Sciences [GL84, Par79, Abs80, GL82, GL86]. Scientific [BBG^{+}95, Nas90, RRV93]. Second [MMP11]. Second-Order [MMP11]. Selective [PS79]. semi [PNOL88, Par92b]. semi-orthogonality [PNOL88, Par92b]. Seminar [RSS96]. Sensitivity [FPD12, Par98a]. sep [Koi09]. sep-inverse [Koi09]. separation [PL92]. September [BR76]. Sets [Par74a]. Seventh [BBG^{+}95, GL86]. sex [Par70]. Shared [BPS94]. Shared-Memory [BPS94]. Shift [PS87a, PS85]. Short [For64, Par64b, Par66d, Par67c, Var66]. should [KP76, KP78a]. SIAM [BBG^{+}95, Par09b, RSS96, Lew94]. sich [KP78b]. sided [WW20]. Simmetrichnaya [Par83a]. simple [RBS66]. Singular [BPS94, FP92a, Par66d, PF94b, PF95, FP92b, FP93a, FP93c, FP94, FP95, PF94a]. Sixth [GL84]. Snowbird [Lew94]. sobstvennykh [Par83a]. Soc [HP92b]. Software [Par84, PW75, PW77, Par83b]. Solution [BP00, PR70, PD97, BPV00, BP03, NOPT80, NOPT83a, NOPT83b, Par76b, Par77a, Par81c]. Solutions [Par00c, BPV06, PPV93, PPv95]. solve [Par80a, Par81d]. Solver [LNOP82, PNOL81]. Solving [BP71, NNOP86, Par80b]. Some [HP92b, Par74b, Par89, Par92c]. Sparse [BPS94, BR76, Par74a, Par84, GP88, GP90, Par83b, BR76]. Special [BP03, BPV06]. Spectral [NOPEJ87, Par98a, NOP84, Par03b]. Spectrum [KPRV97, FP09, PV09]. splitting [NOP85]. Springer [Par79]. Springer-Verlag [Par79]. square [PF75]. state [Par87c]. state-of-the-art [Par87c]. Steger [PT81a]. Steinberg [PT81a]. Stewart [Par81a]. Stiefel [Par74c]. Stochastic [PL82, PL81]. Strategies [PS87a, PS85]. structural [Par87c]. structured [Par10]. structures [PNON84, ZPP05b]. Studies [Par79]. Study [MGD93, Ard80]. submatrices [Par96c]. Subset [MPV05]. subsets [MPV06]. Subspace [VP11, NOPT80, NOPT83a, Par10]. subspaces [PPV93, PPv95, Par96a, WW20]. successive [BPW05]. Summer [RSS96]. Supercomputer [Num85]. SVD [Par05]. swap [Par77b, PN87]. Symmetric [BP71, BKP76, CW85, DMPV07a, DMPV07b, KP74, KPRV97, PR70, Par74c, Par80c, PR81, Par91, Par94, Par98b, PD00, PKS02, DMPV08, DP04a, MVDP09, Par67e, Par80b, PNO82a, PWW83, Par83a, PW84, Par03a]. Symposium [BR76, GL82, GL84, GL86, GGMP88, KvSR90, Gre72, BOW77]. System [PR70, FPD95]. Systems [BP71, MMP11, BPW05, Par76b, Par77a, Par80b, PH97].

Tagung [Alb91]. Technical [For64, Par64b, Par66d, Par67c, Var66]. techniques [NOP85]. Tensor [ZPP05a, ZPP05b]. Testing [DMPV07b, MVDP09]. Tests [For64]. Their [Par74a, Par62]. theorem [WW20, Par09a]. Theory [CW85, PP73, Par92c, Par09b, BIP97, HP92b, Par81c, PS87b, Par89, SP09, SP88]. there [Par72a]. Tight [PV04, Par96c]. tightly [Par96a]. Time [MGD93]. Topological [ZPP05a, ZPP05b]. Tracking [PR81]. transform [Par82b]. Transformation [MMP11, NOPEJ87, Par66d, LP88, NOP84]. translated [Par74c]. transposition [DP10]. Traub [HP92b]. treatment [Alb91]. Triangular [Par74d, PW75, Par76a, BEK97, FP95, PW77]. tributes [BIP97]. Tridiagonal [DMPV07a, PH78, Par92a, PL93, PDF16, DMPV08, DP04a, FPD95, FP09, FPD12, FP22, HP77, HP78, MVDP09, Par67e, PNO82a, Par90c, Par03a]. Tridiagonals [PNO85, PD00, PWW83, PNO83, PW84, Par96a, Par00b]. triple [FP22]. Triplets [BPS94]. Two [Par82a, Par69, WW20]. two-sided [WW20]. Type [Par64a].

U.S [BOW77]. Understand [Par94]. uniform [BP66]. University [Gre72]. unsymmetric [FPD12, PT81b, PTL84, PTL85]. update [PNO82a]. Updating [PNO85, PNO83]. USA [RRV93]. Use [Par64a, PNO85, PC88, PC90b, PNO83, Par96c]. User [Par81a]. Using [NOPR88, NOP85, PNOR87]. Utah [Lew94, RSS96].

V [GL82]. valeurs [Par73a]. Values [FP92a, FP92b, FP93a, FP93c, FP94, FP95, PS08]. varied [Par05]. Vector [PNOJ85]. vectors [FP93c, FP95, PNOL88, Par92b, PF94a, PF94b, PF95]. Verlag [Par79]. verlassen [KP78b]. Versailles [GL82, GL84, GL86]. versions [Par97]. versus [NOPT80, NOPT83a]. VI [GL84]. via [Par82b, PF94b, PF95]. VII [GL86]. Vol [Par72b]. Volume [CW85].

W [Par81a]. Wallace [GP91]. Wallach [SP09]. way [FPD95]. were [GP11]. whose [PR70]. Wilkinson [Par66a, Par72b, FP20, Par87a, Par90a, PD97]. William [Bun95]. Willoughby [Par74a]. Winograd [Par82b]. Wisconsin [Gre72]. Without [CFP77, CFP75, Par96b]. Workshop [Alb91, BP00]. Woźniakowski [HP92b].

xi [Par74c]. xiv [Par79]. xx [Par09b].

York [Par79].

znachenii [Par83a].

References

Absi:1980:NME

[Abs80] Élie Absi, editor. Numerical methods for engineering: 2nd International Congress = Méthodes numériques dans les sciences de l’ingénieur: 2e Congrès international. Dunod, Paris, France, 1980. ISBN 2-04-012165-X (vol. 1), 2-04-012194-3 (vol. 2). LCCN TA329 .C64 1980; TA329 .C64 1980.

Albrecht:1991:NTE

[Alb91] J. (Julius) Albrecht, editor. Numerical treatment of eigenvalue problems: Workshop in Oberwolfach, February 25-March 3, 1990 = Numerische Behandlung von Eigenwertaufgaben: Tagung in Oberwolfach, 25. Februar–3. März 1990, volume 96 of International series of numerical mathematics; Numerical treatment of eigenvalue problems. Birkhäuser, Cambridge, MA, USA; Berlin, Germany; Basel, Switzerland, 1991. ISBN 3-7643-2575-5.

Arden:1980:WCA

[Ard80] Bruce W. Arden, editor. What can be automated?: The computer science and engineering research study (COSERS), volume 3 of The MIT Press series in computer science. MIT Press, Cambridge, MA, USA, 1980. ISBN 0-262-01060-7. 934 pp. LCCN QA76 .W49.

Bailey:1995:PSS

[BBG^{+}95] D. H. Bailey, P. E. Bjorstad, J. R. Gilbert, M. V. Mascagni, R. S. Schreiber, H. D. Simon, V. J. Torczon, and L. T. Watson, editors. Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing (February 15–17, 1995, San Francisco, CA). Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1995. ISBN 0-89871-344-7. LCCN QA76.58.S55 1995.

Brown:1994:PCL

[BCEP94] J. David Brown, Moody T. Chu, Donald C. Ellison, and Robert J. Plemmons, editors. Proceedings of the Cornelius Lanczos International Centenary Conference, Raleigh, North Carolina, December 12–17, 1993, volume 73 of Proceedings in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1994. ISBN 0-89871-339-0. LCCN QC19.2 .C67 1993.

Bakkaloglu:1997:PPA

[BEK97] B. Bakkaloğlu, K. Erciyeş, and Ç. K. Koç. A parallelization of Parlett’s algorithm for functions of triangular matrices. Parallel Algorithms and Applications, 11(1–2):61–69, May 1997. CODEN

PAAPEC. ISSN 1063-7192. URL http://www.math.utah.edu/
pub/tex/bib/parallelalgorithmsappl.bib.

Buhmann:1997:ATO

[BIP97] M. D. (Martin Dietrich) Buhmann, A. Iserles, and M. J. D. (Michael James David) Powell, editors. Approximation theory and optimization: tributes to M. J. D. Powell. Cambridge University Press, Cambridge, UK, 1997. ISBN 0-521-58190-7 (hardback). LCCN QA221 .A655 1997.

Bunch:1976:DSM

[BKP76] James R. Bunch, Linda Kaufman, and Beresford N. Parlett. Decomposition of a symmetric matrix. Numerische Mathematik, 27 (1):95–109, 1976. CODEN NUMMA7. ISSN 0029-599X (print),

0945-3245 (electronic).  URL http://www.math.utah.edu/
pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;   http:/
/www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.
bib;   http://www.math.utah.edu/pub/tex/bib/gvl.bib;
http://www.math.utah.edu/pub/tex/bib/nummath.bib.

Bathe:1977:FCA

[BOW77] Klaus-Jürgen Bathe, J. Tinsley (John Tinsley) Oden, and Edward L. Wilson, editors. Formulations and computational algorithms in finite element analysis: U.S.–Germany symposium. MIT Press, Cambridge, MA, USA, 1977. ISBN 0-262-02127-7. LCCN TA347.F5 F67; TA347.F5 F67.

Buchanan:1966:UCM

[BP66] M. L. Buchanan and B. N. Parlett. The uniform convergence of matrix powers. Numerische Mathematik, 9:51–54, 1966. CODEN NUMMA7. ISSN 0029-599X (print), 0945-3245 (electronic). URL

http://www.math.utah.edu/pub/tex/bib/nummath.bib.

Bunch:1971:DMS

[BP71] James R. Bunch and Beresford N. Parlett. Direct methods for solving symmetric indefinite systems of linear equations. SIAM Journal on Numerical Analysis, 8(4):639–655, December 1971. CODEN SJNAAM. ISSN 0036-1429 (print),

1095-7170 (electronic).  URL http://www.math.utah.edu/
pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;   http:/
/www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.
bib;   http://www.math.utah.edu/pub/tex/bib/gvl.bib;
http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib.

Barlow:2000:PIW

[BP00] Jesse L. Barlow and Beresford N. Parlett, editors. Proceedings of the International Workshop on Accurate Solution of Eigenvalue Problems, Linear Algebra and its Applications. Elsevier, Amsterdam, The Netherlands, 2000. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (electronic). Held at Pennsylvania State University, University Park, PA, July 20–23, 1998, Linear Algebra Appl. 309 (2000), no. 1–3.

Barlow:2003:SIA

[BP03] Jesse L. Barlow and Beresford N. Parlett, editors. Special issue on accurate solution of eigenvalue problems. Elsevier Science, Inc., Amsterdam, The Netherlands, 2003. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (electronic). iv + 425 pp. Including papers from the 3rd International Workshop (IWASEP) held in Hagen, July 3–6, 2000, Linear Algebra Appl. 358 (2003).

Berman:1981:DSO

[BPP81] A. Berman, B. N. Parlett, and R. J. Plemmons. Diagonal scaling to an orthogonal matrix. SIAM Journal on Algebraic and Discrete Methods, 2(1):57–65, March 1981. CODEN SJAMDU. ISSN 0196-5212 (print), 2168-345X (electronic). URL http://

www.math.utah.edu/pub/tex/bib/siamjalgdiscmeth.bib.

Berry:1994:CES

[BPS94] M. W. Berry, B. N. Parlett, and A. H. Sameh. Computing extremal singular triplets of sparse matrices on a shared-memory multiprocessor. International Journal of High Speed Computing (IJHSC), 6(2):239–276, 1994. CODEN IHSCEZ. ISSN

0129-0533. URL http://www.worldscientific.com/doi/abs/
10.1142/S0129053394000123.

Barlow:2000:ASE

[BPV00] J. L. Barlow, Beresford N. Parlett, and Krešimir Veselić. The accurate solution of eigenvalue problems. Linear Algebra and its Applications, 309(1–3):1–2, April 15, 2000. CO-DEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (elec-

tronic).  URL http://www.elsevier.nl/gej-ng/10/30/19/
126/25/25/abstract.html;   http://www.elsevier.nl/gej-
ng/10/30/19/126/25/25/article.pdf;   http://www.math.utah.
edu/pub/tex/bib/linala2000.bib.

Barlow:2006:PSI

[BPV06] Jesse L. Barlow, Beresford N. Parlett, and Kresimir Veselić. Preface [special issue on accurate solutions of eigenvalue problems]. Linear Algebra and its Applications, 417(2–3):381, 2006. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (electronic).

Bai:2005:GSO

[BPW05] Zhong-Zhi Bai, Beresford N. Parlett, and Zeng-Qi Wang. On generalized successive overrelaxation methods for augmented linear systems. Numerische Mathematik, 102(1):1–38, November 2005. CODEN NUMMA7. ISSN 0029-599X (print), 0945-3245 (elec-

tronic). URL http://www.springerlink.com/openurl.asp?
genre=article&issn=0029-599X&volume=102&issue=1&spage=
1.

Bunch:1976:SMC

[BR76] James R. Bunch and Donald J. Rose, editors. Sparse Matrix Computations: Proceedings of the Symposium on Sparse Matrix Computations at Argonne National Laboratory on September 9– 11, 1975. Academic Press, New York, NY, USA, 1976. ISBN 0-12-141050-1. LCCN QA188 .S989 1975.

Bunch:1995:EDB

[Bun95] James R. Bunch. Editorial: Dedicated to Beresford Parlett and William Kahan. Numerical Linear Algebra with Applications, 2 (2):85, 1995. CODEN NLAAEM. ISSN 1070-5325 (print), 1099-1506 (electronic).

Chan:1975:PCC

[CFP75] Sai-Pak Chan, R. Feldman, and Beresford N. Parlett. A program to compute the condition numbers of matrix eigenvalues without computing eigenvectors. Memorandum ERL-M517, Electronics Research Laboratory, College of Engineering, University of California, Berkeley, Berkeley, CA, USA, 1975. 44 pp.

Chan:1977:APC

[CFP77] S. P. Chan, R. Feldman, and B. N. Parlett. Algorithm 517: A program for computing the condition numbers of matrix eigenvalues without computing eigenvectors [F2]. ACM Transactions on Mathematical Software, 3(2):186–203, June 1977. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic).

Cox:1990:RNC

[CH90] M. G. Cox and S. Hammarling, editors. Reliable numerical computation. Oxford University Press, Walton Street, Oxford OX2 6DP, UK, 1990. ISBN 0-19-853564-3. LCCN QA297 .R435 1990. US$75.00. Based on papers from a conference in honour of the late James Hardy Wilkinson (died Sunday 5th October 1986) held at National Physical Laboratory, Teddington, Middlesex, UK, 8th– 10th July 1987.

Cullum:1985:LAL

[CW85] Jane K. Cullum and Ralph A. Willoughby. Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Volume I Theory. Birkhäuser, Cambridge, MA, USA; Berlin, Germany; Basel, Switzerland, 1985. ISBN 0-8176-3058-9. xiv + 273

pp. URL http://www.math.utah.edu/pub/bibnet/subjects/
acc-stab-num-alg.bib.

Demmel:2007:PNL

[DDP^{+}07] James W. Demmel, Jack J. Dongarra, Beresford N. Parlett, William Kahan, Ming Gu, David S. Bindel, Yozo Hida, Xiaoye S. Li, Osni A. Marques, E. Jason Riedy, Christof Vömel, Julien Langou, Piotr Luszczek, Jakub Kurzak, Alfredo Buttari, Julie Langou, and Stanimire Tomov. Prospectus for the next LAPACK and ScaLAPACK libraries. LAPACK Working Note 181, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, March 11, 2007. URL http://www.

netlib.org/lapack/lawnspdf/lawn181.pdf.

Davies:2003:SPA

[DH03] P. I. Davies and N. J. Higham. A Schur–Parlett algorithm for computing matrix functions. SIAM Journal on Matrix Analysis and Applications, 25(2):464–485, ???? 2003. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic).

Demmel:2007:PAL

[DMPV07a] James W. Demmel, Osni A. Marques, Beresford N. Parlett, and Christof Vömel. Performance and accuracy of LAPACK’s symmetric tridiagonal eigensolvers. LAPACK Working Note 183, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA, April 2007. URL

http://www.netlib.org/lapack/lawnspdf/lawn183.pdf.

Demmel:2007:TIL

[DMPV07b] James W. Demmel, Osni A. Marques, Beresford N. Parlett, and Christof Vömel. A testing infrastructure for LAPACK’s symmetric eigensolvers. LAPACK Working Note 182, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA, April 2007. URL http://www.

netlib.org/lapack/lawnspdf/lawn182.pdf.

Demmel:2008:PAL

[DMPV08] James W. Demmel, Osni A. Marques, Beresford N. Parlett, and Christof Vömel. Performance and accuracy of LAPACK’s symmetric tridiagonal eigensolvers. SIAM Journal on Scientific Computing, 30(3):1508–1526, 2008. CODEN SJOCE3. ISSN 1064-8275 (print), 1095-7197 (electronic).

Dhillon:2002:OER

[DP02] Inderjit S. Dhillon and Beresford N. Parlett. Orthogonal eigenvectors and relative gaps. LAPACK Working Note 154, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, August 2002.

URL http://www.math.utah.edu/pub/tex/bib/lawn.bib;
http://www.netlib.org/lapack/lawns/lawn154.ps;   http:
//www.netlib.org/lapack/lawnspdf/lawn154.pdf. UT-CS-02-

474, August 2002 Published in [DP04b].

Dhillon:2003:OER

[DP03] Inderjit S. Dhillon and Beresford N. Parlett. Orthogonal eigenvectors and relative gaps. SIAM Journal on Matrix Analysis and Applications, 25(3):858–899, July 2003. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic). URL http://epubs.

siam.org/sam-bin/dbq/article/37011;   http://www.math.
utah.edu/pub/tex/bib/lawn.bib;   http://www.math.utah.
edu/pub/tex/bib/siamjmatanaappl.bib. See original LAPACK

Working note in [DP02].

Dhillon:2004:MRC

[DP04a] Inderjit S. Dhillon and Beresford N. Parlett. Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices. Linear Algebra and its Applications, 387(1):1–28, August 1, 2004. CODEN LAAPAW. ISSN 0024-3795 (print),

1873-1856 (electronic). URL http://www.math.utah.edu/pub/
tex/bib/linala2000.bib.

Dhillon:2004:OER

[DP04b] Inderjit S. Dhillon and Beresford N. Parlett. Orthogonal eigenvectors and relative gaps. SIAM Journal on Matrix Analysis and Applications, 25(3):858–899, July 2004. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic). URL http://epubs.

siam.org/sam-bin/dbq/article/37011. See original LAPACK

Working note in [DP02].

Dubrulle:2010:RTM

[DP10] A. A. Dubrulle and B. N. Parlett. Revelations of a transposition matrix. Journal of Computational and Applied Mathematics, 233(5):1217–1219, January 1, 2010. CODEN JCAMDI. ISSN 0377-0427 (print), 1879-1778 (electronic). URL http://www.

sciencedirect.com/science/article/pii/S0377042709001745.

Dhillon:2004:DIM

[DPV04] Inderjit S. Dhillon, Beresford N. Parlett, and Christof Vömel. The design and implementation of the MRRR algorithm. LAPACK Working Note 162, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, February 2004.

URL http://www.math.utah.edu/pub/tex/bib/lawn.bib;
http://www.netlib.org/lapack/lawns/lawn162.ps;   http:
//www.netlib.org/lapack/lawnspdf/lawn162.pdf. UT-CS-04-

541, December, 2004.

Dhillon:2005:GMM

[DPV05] Inderjit S. Dhillon, Beresford N. Parlett, and Christof Vömel. Glued matrices and the MRRR algorithm. SIAM Journal on Scientific Computing, 27(2):496–510, March 2005. CODEN SJOCE3. ISSN 1064-8275 (print), 1095-7197 (electronic). URL http://

epubs.siam.org/sam-bin/dbq/article/62074.

Dhillon:2006:DIM

[DPV06] Inderjit S. Dhillon, Beresford N. Parlett, and Christof Vömel. The design and implementation of the MRRR algorithm. ACM Transactions on Mathematical Software, 32(4):533–560, December 2006. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic).

Edelman:1995:PMN

[EM95] Alan Edelman and Walter F. Mascarenhas. On Parlett’s matrix norm inequality for the Cholesky decomposition. Numerical Linear Algebra with Applications, 2(3):243–250, 1995. CODEN NLAAEM. ISSN 1070-5325 (print), 1099-1506 (electronic). URL http://www.

math.utah.edu/pub/tex/bib/numlinaa.bib.

Forsythe:1964:TPA

[For64] George E. Forsythe. Tests of Parlett’s ALGOL eigenvalue procedure Eig3 (in Technical Notes and Short Papers). Mathematics of Computation, 18(87):486–487, July 1964. CODEN MCMPAF. ISSN 0025-5718 (paper), 1088-6842 (electronic). URL http://

www.math.utah.edu/pub/tex/bib/mathcomp1960.bib.

Fernando:1992:ASVa

[FP92a] K. Vince Fernando and Beresford N. Parlett. Accurate singular values and differential qd algorithms. Technical Report TR2/92, NAG Ltd., Oxford, UK, July 1992. ???? pp. URL http://www.math.

utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib. To

appear in Numer. Math.

Fernando:1992:ASVb

[FP92b] K. Vince Fernando and Beresford N. Parlett. Accurate singular values and differential qd algorithms. Technical Report PAM-554, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, July 1992.

Fernando:1993:ASVc

[FP93a] K. Vince Fernando and Beresford N. Parlett. Accurate singular values and differential qd algorithms. In Moonen et al. [MGD93], pages 371–374. ISBN 0-7923-2151-0. LCCN

QA185.D37 L56 1993. 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.

Fernando:1993:DA

[FP93b] K. Vince Fernando and Beresford N. Parlett. Differential qd algorithms. In Reichel et al. [RRV93], pages 75–100. ISBN 3-11-013784-4. LCCN QA184.C655 1993.

Fernando:1993:ICA

[FP93c] K. Vince Fernando and Beresford N. Parlett. Implicit Cholesky algorithms for singular values and vectors. Technical Report PAM-587, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, August 1993.

Fernando:1994:ASV

[FP94] K. Vince Fernando and Beresford N. Parlett. Accurate singular values and differential qd algorithms. Numerische Mathematik, 67 (2):191–229, March 1994. CODEN NUMMA7. ISSN 0029-599X (print), 0945-3245 (electronic). URL http://link.springer.de/

link/service/journals/00211/bibs/4067002/40670191.htm;
 http://science.springer.de/nmee/bibs/4067002/40670191.
htm;   http://www.math.utah.edu/pub/tex/bib/nummath.bib.

Fernando:1995:ICA

[FP95] K. Vince Fernando and Beresford N. Parlett. Implicit Cholesky algorithms for singular values and vectors of triangular matrices. Numerical Linear Algebra with Applications, 2(6):507–531, 1995. CO-DEN NLAAEM. ISSN 1070-5325 (print), 1099-1506 (electronic).

URL http://www.math.utah.edu/pub/tex/bib/numlinaa.bib.

Ferreira:2009:CAO

[FP09] Carla Ferreira and Beresford Parlett. Convergence of LR algorithm for a one-point spectrum tridiagonal matrix. Numerische Mathematik, 113(3):417–431, September 2009. CO-DEN NUMMA7. ISSN 0029-599X (print), 0945-3245 (elec-

tronic). URL http://www.springerlink.com/openurl.asp?
genre=article&issn=????&volume=113&issue=3&spage=417.

Ferreira:2020:EWM

[FP20] Carla Ferreira and Beresford Parlett. Eigenpairs of Wilkinson matrices. SIAM Journal on Matrix Analysis and Applications, 41(3): 1388–1415, ???? 2020. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic).

Ferreira:2022:RTD

[FP22] Carla Ferreira and Beresford Parlett. A real triple dqds algorithm for the nonsymmetric tridiagonal eigenvalue problem. Numerische Mathematik, 150(2):373–422, February 2022. CODEN NUMMA7. ISSN 0029-599X (print), 0945-3245 (electronic). URL http://

link.springer.com/article/10.1007/s00211-021-01254-z.

Fernando:1995:WFM

[FPD95] K. Vince Fernando, Beresford N. Parlett, and Inderjit Dhillon. A way to find the most redundant equation in a tridiagonal system. Technical Report PAM-635, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, May 1995.

Ferreira:2012:SEU

[FPD12] Carla Ferreira, Beresford Parlett, and Froilán M. Dopico. Sensitivity of eigenvalues of an unsymmetric tridiagonal matrix. Numerische Mathematik, 122(3):527–555, November 2012. CODEN NUMMA7. ISSN 0029-599X (print), 0945-3245 (electronic). URL

http://www.springerlink.com/openurl.asp?genre=article&
issn=0029-599X&volume=122&issue=3&spage=527.

Glowinski:1988:FIS

[GGMP88] Roland Glowinski, Gene H. Golub, Gérard Meurant, and Jacques Périaux, editors. First International Symposium on Domain Decomposition Methods for Partial Differential Equations: Proceedings of the First International Symposium on Domain Decomposition Methods for Partial Differential Equations, Ecole Nationale des Ponts et Chaussées, Paris, France, January 7–9, 1987. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1988. ISBN 0-89871-220-3. LCCN QA402.2 .I571 1987.

Glowinski:1982:CMA

[GL82] R. Glowinski and Jacques Louis Lions, editors. Computing methods in applied sciences and engineering, V: proceedings of the Fifth International Symposium on Computing Methods in Applied Sciences and Engineering, Versailles, France, December 14–18, 1981. North-Holland, Amsterdam, The Netherlands, 1982. ISBN 0-444-86450-4. LCCN QA297 .E53 1981.

Glowinski:1984:CMA

[GL84] R. Glowinski and J.-L. Lions, editors. Computing Methods in Applied Sciences and Engineering, VI: Proceedings of the Sixth International Symposium on Computing Methods in Applied Sciences and Engineering, Versailles, France, December 12–16, 1983. North-Holland, Amsterdam, The Netherlands, 1984. ISBN 0-444-87597-2. LCCN QA297 .I57 1983.

Glowinski:1986:CMA

[GL86] R. (Roland) Glowinski and Jacques Louis Lions, editors. Computing methods in applied sciences and engineering, VII: proceedings of the Seventh International Symposium on Computing Methods in Applied Sciences and Engineering, Versailles, France, December 9–13, 1985. North-Holland, Amsterdam, The Netherlands, 1986. ISBN 0-444-70059-5. LCCN TA345.

Gear:1979:NCR

[GOP^{+}79] C. W. Gear, J. M. Ortega, B. Parlett, J. R. Rice, M. Schultz, L. F. Shampine, and P. Wolfe. Numerical computation: A report on past, present, and future research. ACM SIGNUM Newsletter, 14 (si-1):1–48, February 1979. CODEN SNEWD6. ISSN 0163-5778 (print), 1558-0237 (electronic). Also published in [GOP^{+}80].

Gear:1980:NCR

[GOP^{+}80] C. W. Gear, J. M. Ortega, B. Parlett, J. R. Rice, M. Schultz, L. F. Shampine, and P. Wolfe. Numerical computation: A report on past, present, and future research. In Arden [Ard80], pages 51– 136. ISBN 0-262-01060-7. LCCN QA76 .W49. Also published in [GOP^{+}79].

Gao:1988:CCS

[GP88] F. Gao and Beresford N. Parlett. Communication cost of sparse Cholesky factorization on a hypercube. Technical Report PAM-436, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, December 1988.

Gao:1990:NCA

[GP90] Feng Gao and Beresford N. Parlett. A note on communication analysis of parallel sparse Cholesky factorization on a hypercube. Parallel Computing, 16(1):59–60, November 1990. CODEN PACOEJ. ISSN 0167-8191 (print), 1872-7336 (electronic). URL http://www.

math.utah.edu/pub/tex/bib/parallelcomputing.bib.

Golub:1991:DJW

[GP91] G. Golub and B. Parlett. Dedication to J. Wallace Givens. SIAM Journal on Matrix Analysis and Applications, 12(1):U1, January 1991. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic).

Gutknecht:2011:HWA

[GP11] Martin H. Gutknecht and Beresford N. Parlett. From qd to LR, or, how were the qd and LR algorithms discovered? IMA Journal of Numerical Analysis, 31(3):741–754, July 2011. CO-DEN IJNADH. ISSN 0272-4979 (print), 1464-3642 (electronic).

URL http://imajna.oxfordjournals.org/content/31/3/741.
full.pdf+html.

Greville:1972:PDP

[Gre72] T. N. E. (Thomas Nall Eden) Greville, editor. Population dynamics: proceedings of a symposium conducted by the Mathematics Research Center, the University of Wisconsin, Madison, June 19– 21, 1972, volume 29 of Mathematics Research Center Publications. Academic Press, New York, NY, USA, 1972. ISBN 0-12-302940-6. Some catalogs show ISBN 0-12-302940-1 with invalid checksum.

Hoffman:1977:NPG

[HP77] W. Hoffman and Beresford N. Parlett. A new proof of global convergence for the tridiagonal QL algorithm. Memorandum UCB/ERL M77/48, Electronics Research Laboratory, College of Engineering, University of California, Berkeley, Berkeley, CA, USA, July 7, 1977. 18 pp.

Hoffmann:1978:NPG

[HP78] W. Hoffmann and B. N. Parlett. A new proof of global convergence for the tridiagonal QL algorithm. SIAM Journal on Numerical Analysis, 15(5):929–937, October 1978. CODEN SJ-NAAM. ISSN 0036-1429 (print), 1095-7170 (electronic). URL

http://www.math.utah.edu/pub/tex/bib/gvl.bib;   http:/
/www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib.

Hill:1991:RIP

[HP91] R. O. Hill and Beresford N. Parlett. Refined interlacing properties. Technical Report PAM-517, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, January 1991.

Hill:1992:RIP

[HP92a] R. O. Hill, Jr. and B. N. Parlett. Refined interlacing properties. SIAM Journal on Matrix Analysis and Applications, 13(1):239– 247, January 1992. CODEN SJMAEL. ISSN 0895-4798 (print),

1095-7162 (electronic). URL http://www.math.utah.edu/pub/
tex/bib/siamjmatanaappl.bib.

Hirsch:1992:ERS

[HP92b] Morris W. Hirsch and Richard S. Palais. Editors’ remarks: “Some basic information on information-based complexity theory” [Bull. Amer. Math. Soc. (N.S.) 26 (1992), no. 1, 3–27; MR1102755 (94e:68077a)] by B. N. Parlett and “Perspectives on informationbased complexity” [Bull. Amer. Math. Soc. (N.S.) 26 (1992), no. 1, 29–52; MR1102756 (94e:68077b)] by J. F. Traub and H. Woźniakowski. Bulletin of the American Mathematical Society (new series), 26(1):1–2, 1992. CODEN BAMOAD. ISSN 0273-0979 (print), 1088-9485 (electronic).

Iserles:1995:AN

[Ise95] A. Iserles, editor. Acta Numerica 1995. Cambridge University Press, Cambridge, UK, 1995. ISBN 0-521-48255-0. 491 pp.

Koikari:2009:ABS

[Koi09] Souji Koikari. Algorithm 894: On a block Schur–Parlett algorithm for φ-functions based on the sep-inverse estimate. ACM Transactions on Mathematical Software, 36(2):12:1–12:20, March 2009. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic).

Kahan:1974:ALA

[KP74] W. Kahan and B. N. Parlett. An analysis of Lanczos algorithms for symmetric matrices. Technical Report ERL-M467, Electronics Research Laboratory, College of Engineering, University of California, Berkeley, Berkeley, CA, USA, 1974. URL http:/

/www.math.utah.edu/pub/bibnet/authors/k/kahan-william-
m.bib;   http://www.math.utah.edu/pub/tex/bib/gvl.bib.

Kahan:1976:HFS

[KP76] W. Kahan and B. N. Parlett. How far should you go with the Lanczos process? In Bunch and Rose [BR76], pages 131–144. ISBN 0-12-141050-1. LCCN QA188 .S989 1975.

Kahan:1977:CYC

[KP77] W. M. Kahan and B. N. Parlett. Can you count on your calculator? Memorandum UCB/ERL M77/21, Electronics Research Laboratory, College of Engineering, University of California, Berkeley, Berkeley, CA, USA, April 6, 1977. ii + 28 pp. URL http:/

/www.math.utah.edu/pub/bibnet/authors/k/kahan-william-
m.bib;   http://www.math.utah.edu/pub/bibnet/subjects/

acc-stab-num-alg.bib. German Transl. Published In: Jahrbuch Überblicke Mathematik 1978, Ed. by B. Fuchssteiner and others, Bibliographisches Institut, Mannheim-Wien-Zürich, 199–216, 1978.

Kahan:1978:HFS

[KP78a] W. Kahan and B. N. Parlett. How far should you go with the Lanczos process? Memorandum UCB/ERL M78/48, Electronics Research Laboratory, College of Engineering, University of California, Berkeley, Berkeley, CA, USA, 1978. 16 pp.

Kahan:1978:KSI

[KP78b] W. Kahan and B. N. Parlett. Können Sie sich auf Ihren Rechner verlassen? (German) [can you count on your calculator?]. Jahrbuch Überblicke Mathematik, ??:199–216, 1978.

Kahan:1982:RBA

[KPJ82] W. Kahan, B. N. Parlett, and E. Jiang. Residual bounds on approximate eigensystems of nonnormal matrices. SIAM Journal on Numerical Analysis, 19(3):470–484, June 1982. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic). URL http:/

/www.math.utah.edu/pub/bibnet/authors/k/kahan-william-
m.bib;   http://www.math.utah.edu/pub/bibnet/subjects/
acc-stab-num-alg.bib;   http://www.math.utah.edu/pub/tex/
bib/gvl.bib;   http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.
bib.

Kandic:1997:ECH

[KPRV97] Dragan B. Kandić, Beresford Parlett, Branimir D. Reljin, and Petar M. Vasić. Explicit construction of hyperdominant symmetric matrices with assigned spectrum. Linear Algebra and its Applications, 258(1–3):41–51, June 1997. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (electronic). URL http:

//www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/
browse/browse.cgi?year=1997&volume=258&issue=1-3&aid=9600161;
 http://www.math.utah.edu/pub/tex/bib/linala1990.bib.

Kaashoek:1990:PIS

[KvSR90] M. A. Kaashoek, J. H. van Schuppen, and A. C. M. Ran, editors. Proceedings of the International Symposium MTNS-89, volume 3–5 of Progress in systems and control theory. Birkhäuser Boston Inc., Cambridge, MA, USA, 1990. ISBN 0-8176-3469-X (vol 1), 0-8176-3470-3 (vol. 2), 0-8176-3471-1 (vol. 3), 0-8176-3468-1 (set). LCCN QA402 .P766 1989.

Lewis:1994:ALA

[Lew94] John G. Lewis, editor. Applied Linear Algebra: Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, Snowbird, Utah, June 15–18, 1994. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1994. ISBN 0-89871-336-6. LCCN QA184.S58 1994.

Li:2014:IDA

[LGP14] Shengguo Li, Ming Gu, and Beresford N. Parlett. An improved DQDS algorithm. SIAM Journal on Scientific Computing, 36(3): C290–C308, ???? 2014. CODEN SJOCE3. ISSN 1064-8275 (print), 1095-7197 (electronic).

Li:1982:FSF

[LNOP82] M. R. Li, B. Nour-Omid, and B. N. Parlett. A fast solver free of fill-in for finite-element problems. SIAM Journal on Numerical Analysis, 19(6):1233–1242, December 1982. CODEN SJ-NAAM. ISSN 0036-1429 (print), 1095-7170 (electronic). URL

http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-
num-alg.bib;   http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.
bib.

Le:1988:FIT

[LP88] J. Le and Beresford N. Parlett. On the forward instability of the QR transformation. Technical Report PAM-419, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, July 1988.

Liesen:2008:NSP

[LP08] Jörg Liesen and Beresford N. Parlett. On nonsymmetric saddle point matrices that allow conjugate gradient iterations. Numerische Mathematik, 108(4):605–624, February 2008. CODEN NUMMA7. ISSN 0029-599X (print), 0945-3245 (electronic).

Moonen:1993:LAL

[MGD93] Marc S. Moonen, Gene H. Golub, and Bart L. R. De Moor, editors. Linear Algebra for Large Scale and Real-Time Applications: Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3–14, 1992, volume 232 of NATO ASI series. Series E, Applied sciences. Kluwer Academic Publishers, Norwell, MA, USA, and Dordrecht, The Netherlands, 1993.

ISBN 0-7923-2151-0. LCCN QA185.D37 L56 1993. 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.

Morzfeld:2011:TSO

[MMP11] Matthias Morzfeld, Fai Ma, and Beresford N. Parlett. The transformation of second-order linear systems into independent equations. SIAM Journal on Applied Mathematics, 71(4):1026–1043, ???? 2011. CODEN SMJMAP. ISSN 0036-1399 (print), 1095-712X

(electronic). URL http://epubs.siam.org/siap/resource/1/
smjmap/v71/i4/p1026_s1.

McCurdy:1983:ACD

[MNP83] A. McCurdy, K. C. Ng, and Beresford N. Parlett. Accurate computation of divided differences of the exponential function. Technical Report PAM-160, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, June 1983.

McCurdy:1984:ACD

[MNP84] A. McCurdy, K. C. Ng, and B. N. Parlett. Accurate computation of divided differences of the exponential function. Mathematics of Computation, 43(168):501–528, October 1984. CODEN MCMPAF. ISSN 0025-5718 (paper), 1088-6842

(electronic). URL http://www.math.utah.edu/pub/bibnet/
subjects/acc-stab-num-alg.bib;   http://www.math.utah.
edu/pub/tex/bib/mathcomp1980.bib.

Morrell:1969:IPP

[Mor69] A. J. H. Morrell, editor. Information processing 68: proceedings of IFIP congress 1968, organized by the International Federation for Information Processing, Edinburgh, 5–10 August 1968. North-Hol-land, Amsterdam, The Netherlands, 1969. ISBN 0-7204-2032-6. LCCN QA76 .I578.

Marques:2005:SCM

[MPV05] Osni A. Marques, Beresford N. Parlett, and Christof Vömel. Subset computations with the MRRR algorithm. LAPACK Working Note 167, Computer Science Division, University of California, Berkeley, Berkeley, CA, USA, September 26, 2005. 9 pp. URL http://

www.netlib.org/lapack/lawnspdf/lawn167.pdf. Also issued as

Technical Report UCB//CSD-05-1392.

Marques:2006:CES

[MPV06] Osni A. Marques, Beresford N. Parlett, and Christof Vömel. Computations of eigenpair subsets with the MRRR algorithm. Numerical Linear Algebra with Applications, 13(8):643–653, 2006. CO-DEN NLAAEM. ISSN 1070-5325 (print), 1099-1506 (electronic).

Marques:2009:ATI

[MVDP09] Osni A. Marques, Christof Vömel, James W. Demmel, and Beresford N. Parlett. Algorithm 880: a testing infrastructure for symmetric tridiagonal eigensolvers. ACM Transactions on Mathematical Software, 35(1):8:1–8:13, July 2009. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic).

Nash:1990:HSC

[Nas90] Stephen (Stephen G.) Nash, editor. A History of Scientific Computing, ACM Press history series. Addison-Wesley, Reading, MA, USA, 1990. ISBN 0-201-50814-1. LCCN QA76.17 .H59 1990.

Natori:1994:MAP

[NN94] M. Natori and T. Nodera, editors. Matrix analysis and parallel computing, volume 10 of Adv. Numer. Methods Large Sparse Sets Linear Equations. Keio University, Yokohama, Japan, 1994. ISBN ???? LCCN ????

Natvig:1986:ECC

[NNOP86] J. Natvig, B. Nour-Omid, and B. N. Parlett. Effect of the CY-BER 205 on the choice of method for solving the eigenvalue problem (A − λM)x = 0. Journal of Computational and Applied Mathematics, 15(2):137–159, June 1986. CODEN JCAMDI. ISSN 0377-0427 (print), 1879-1778 (electronic). URL http://www.

sciencedirect.com/science/article/pii/0377042786900233.

Nour-Omid:1984:HIS

[NOP84] N. Nour-Omid and B. N. Parlett. How to implement the spectral transformation. Technical Report PAM-224, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley,

CA, USA, 1984. ???? pp. URL http://www.math.utah.edu/pub/
bibnet/subjects/acc-stab-num-alg.bib.

Nour-Omid:1985:EPU

[NOP85] B. Nour-Omid and B. N. Parlett. Element preconditioning using splitting techniques. SIAM Journal on Scientific and Statistical Computing, 6(3):761–770, July 1985. CODEN SIJCD4.

ISSN 0196-5204. URL http://www.math.utah.edu/pub/tex/
bib/siamjscistatcomp.bib.

Nour-Omid:1987:HIS

[NOPEJ87] Bahram Nour-Omid, Beresford N. Parlett, Thomas Ericsson, and Paul S. Jensen. How to implement the spectral transformation. Mathematics of Computation, 48(178):663–673, April 1987. CO-DEN MCMPAF. ISSN 0025-5718 (paper), 1088-6842 (electronic).

URL http://www.math.utah.edu/pub/tex/bib/mathcomp1980.
bib.

Nour-Omid:1988:CLC

[NOPR88] B. Nour-Omid, B. Parlett, and A. Raefsky. Comparison of Lanczos with conjugate gradient using element preconditioning. In Glowinski et al. [GGMP88], pages 250–260. ISBN 0-89871-220-3. LCCN

QA402.2 .I571 1987. URL http://www.math.utah.edu/pub/tex/
bib/ovr.bib.

Nour-Omid:1980:LVS

[NOPT80] Bahram Nour-Omid, Beresford N. Parlett, and Robert L. Taylor. Lanczos versus subspace iteration for solution of eigenvalue problems. Report UC SESM 80-8, Structural Engineering Laboratory, University of California, Berkeley, Berkeley, CA, USA, 1980. 16 pp.

Nour-Omid:1983:LVS

[NOPT83a] Bahram Nour-Omid, Beresford N. Parlett, and Robert L. Taylor. Lanczos versus subspace iteration for solution of eigenvalue problems. International Journal for Numerical Methods in Engineering, 19(6):859–871, 1983. CODEN IJNMBH. ISSN 0029-5981 (print), 1097-0207 (electronic).

Nour-Omid:1983:NLM

[NOPT83b] Bahram Nour-Omid, Beresford N. Parlett, and Robert L. Taylor. A Newton–Lanczos method for solution of nonlinear finite element equations. Computers and Structures, 16(1–4):241–252, 1983. CO-DEN CMSTCJ. ISSN 0045-7949 (print), 1879-2243 (electronic).

Numrich:1985:SA

[Num85] Robert W. Numrich, editor. Supercomputer applications. Plenum Press, New York, NY, USA; London, UK, 1985. ISBN 0-306-42013-9. LCCN QA76.5.S8944 1984a. Proceedings of the Supercomputer Applications Symposium cosponsored by the Purdue University Computing Center, the Purdue Center for Parallel and Vector Computing, and Control Data, held October 31–November 1, 1984, in West Lafayette, Indiana.

Parlett:1962:BML

[Par62] Beresford Neill Parlett. I. Bundles of matrices and the linear independence of their minors; II. Applications of Laguerre’s method to the matrix eigenvalue problem. Ph.D. dissertation, Department of Mathematics, Stanford University, Stanford, CA, USA, 1962. v

+ 118 pp. URL http://www.genealogy.math.ndsu.nodak.edu/
html/id.phtml?id=32898;   http://wwwlib.umi.com/dxweb/
details?doc_no=5023767.

Parlett:1964:DUM

[Par64a] Beresford Parlett. The development and use of methods of LR type. SIAM Review, 6(3):275–295, July 1964. CODEN SIREAD. ISSN 0036-1445 (print), 1095-7200 (electronic).

Parlett:1964:NBA

[Par64b] Beresford Parlett. A note on La Budde’s algorithm (in Technical Notes and Short Papers). Mathematics of Computation, 18(87): 505–506, July 1964. CODEN MCMPAF. ISSN 0025-5718 (paper),

1088-6842 (electronic). URL http://www.math.utah.edu/pub/
tex/bib/mathcomp1960.bib.

Parlett:1964:LMA

[Par64c] Beresford N. Parlett. Laguerre’s method applied to the matrix eigenvalue problem. Mathematics of Computation, 18(87): 464–485, July 1964. CODEN MCMPAF. ISSN 0025-5718 (paper), 1088-6842 (electronic). URL http://www.math.utah.edu/

pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;   http:/
/www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.
bib;   http://www.math.utah.edu/pub/tex/bib/mathcomp1960.
bib.

Parlett:1965:CA

[Par65a] Beresford Parlett. Convergence of the QR algorithm. Numerische Mathematik, 7:187–193, 1965. CODEN NUMMA7. ISSN 0029-599X (print), 0945-3245 (electronic). URL http:

//www.math.utah.edu/pub/tex/bib/gvl.bib;   http://www.
math.utah.edu/pub/tex/bib/nummath.bib.  See correction

[Par67d].

Parlett:1965:MEP

[Par65b] Beresford Parlett. Matrix eigenvalue problems. American Mathematical Monthly, 72(2, part II):59–66, 1965. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). URL

http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-
num-alg-2ed.bib;   http://www.math.utah.edu/pub/bibnet/
subjects/acc-stab-num-alg.bib.

Parlett:1966:BRB

[Par66a] B. N. Parlett. Book review: The Algebraic Eigenvalue Problem (J. H. Wilkinson). SIAM Review, 8(4):543–545, ???? 1966. CODEN SIREAD. ISSN 0036-1445 (print), 1095-7200 (electronic).

Parlett:1966:ADD

[Par66b] Beresford Parlett. Accuracy and dissipation in difference schemes. Communications on Pure and Applied Mathematics (New York), 19(1):111–123, 1966. CODEN CPAMAT, CPMAMV. ISSN 0010-3640 (print), 1097-0312 (electronic).

Parlett:1966:CQR

[Par66c] Beresford Parlett. Convergence of the Q-R algorithm for Hessenberg matrices. Communications of the ACM, 9(7):475, July 1966. CODEN CACMA2. ISSN 0001-0782 (print), 1557-7317 (electronic).

Parlett:1966:SIM

[Par66d] Beresford N. Parlett. Singular and invariant matrices under the QR transformation (in Technical Notes and Short Papers). Mathematics of Computation, 20(96):611–615, October 1966. CODEN MCMPAF. ISSN 0025-5718 (paper), 1088-6842 (electronic). URL

http://www.math.utah.edu/pub/tex/bib/gvl.bib;   http:/
/www.math.utah.edu/pub/tex/bib/mathcomp1960.bib.

Parlett:1967:A

[Par67a] B. N. Parlett. The LU and QR algorithms. In Ralston and Wilf [RW67], pages 116–130. ISBN 0-471-70686-8 (vol. 1), 0-471-70689-2 (vol. 2), 0-471-70690-6 (vol. 3). LCCN ???? URL http://www.

math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib.

Parlett:1967:EA

[Par67b] B. N. Parlett. Eigenvalues, anyone? ACM SIGNUM Newsletter, 1(3):7–8, February 1967. CODEN SNEWD6. ISSN 0163-5778 (print), 1558-0237 (electronic).

Parlett:1967:CDH

[Par67c] Beresford Parlett. Canonical decomposition of Hessenberg matrices (in Technical Notes and Short Papers). Mathematics of Computation, 21(98):223–227, April 1967. CODEN MCMPAF. ISSN 0025-5718 (paper), 1088-6842 (electronic). URL http:

//www.math.utah.edu/pub/tex/bib/gvl.bib;   http://www.
math.utah.edu/pub/tex/bib/mathcomp1960.bib.

Parlett:1967:CCA

[Par67d] Beresford Parlett. Correction to: “Convergence of the QR algorithm”. Numerische Mathematik, 10:163–164, 1967. CODEN NUMMA7. ISSN 0029-599X (print), 0945-3245 (electronic). URL

http://www.math.utah.edu/pub/tex/bib/nummath.bib. See

[Par65a].

Parlett:1967:LEF

[Par67e] Beresford Parlett. Letter to the editor: On finding the eigenvalues of real symmetric tridiagonal matrices. The Computer Journal, 9(4):344–345, February 1967. CODEN CMPJA6. ISSN 0010-4620 (print), 1460-2067 (electronic). URL http://comjnl.

oxfordjournals.org/content/9/4/344.full.pdf.

Parlett:1968:GCB

[Par68] Beresford N. Parlett. Global convergence of the basic QR algorithm on Hessenberg matrices. Mathematics of Computation, 22(104):803–817, October 1968. CODEN MCMPAF. ISSN 0025-5718 (paper), 1088-6842 (electronic). URL http:

//www.math.utah.edu/pub/tex/bib/gvl.bib;   http://www.
math.utah.edu/pub/tex/bib/mathcomp1960.bib.

Parlett:1969:NNM

[Par69] B. N. Parlett. Notes on the number of multiplications required to form the product of two N ×N matrices. ACM SIGNUM Newsletter, 4(2):9–12, June 1969. CODEN SNEWD6. ISSN 0163-5778 (print), 1558-0237 (electronic).

Parlett:1970:EPP

[Par70] Beresford Parlett. Ergodic properties of populations. I. The one sex model. Theoretical Population Biology, 1(??):191–207, 1970. CO-DEN TLPBAQ. ISSN 0040-5809 (print), 1096-0325 (electronic).

Parlett:1971:AAR

[Par71] Beresford N. Parlett. Analysis of algorithms for reflections in bisectors. SIAM Review, 13(2):197–208, ???? 1971. CODEN SIREAD. ISSN 0036-1445 (print), 1095-7200 (electronic). URL

http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-
num-alg-2ed.bib;   http://www.math.utah.edu/pub/bibnet/
subjects/acc-stab-num-alg.bib;   http://www.math.utah.
edu/pub/tex/bib/gvl.bib.

Parlett:1972:CTM

[Par72a] B. Parlett. Can there be a marriage function? In Greville [Gre72], pages 107–135. ISBN 0-12-302940-6. Some catalogs show ISBN 0-12-302940-1 with invalid checksum.

Partlett:1972:BRB

[Par72b] B. Partlett. Book review: Handbook for Automatic Computation, Vol. II, Linear Algebra (J. H. Wilkinson and C. Reinsch). SIAM Review, 14(4):658–661, ???? 1972. CODEN SIREAD. ISSN 0036-1445 (print), 1095-7200 (electronic).

Parlett:1973:PGM

[Par73a] B. N. Parlett. Présentation géométrique des méthodes de calcul des valeurs propres. (French) [Geometric presentation of methods for calculation of eigenvalues]. Numerische Mathematik, 21 (3):223–233, 1973. CODEN NUMMA7. ISSN 0029-599X (print),

0945-3245 (electronic). URL http://www.math.utah.edu/pub/
tex/bib/nummath.bib.

Parlett:1973:NHM

[Par73b] Beresford Parlett. Normal Hessenberg and moment matrices. Linear Algebra and its Applications, 6(??):37–43, ???? 1973. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856

(electronic). URL http://www.sciencedirect.com/science/
article/pii/0024379573900050.

Parlett:1974:BRB

[Par74a] B. N. Parlett. Book review: Large Sparse Sets of Linear Equations (J. K. Reid, ed.); Sparse Matrices and Their Applications (Donald J. Rose and Ralph A. Willoughby, ed.). SIAM Review, 16(3):396– 398, ???? 1974. CODEN SIREAD. ISSN 0036-1445 (print), 1095-7200 (electronic).

Parlett:1974:RQI

[Par74b] B. N. Parlett. The Rayleigh quotient iteration and some generalizations for nonnormal matrices. Mathematics of Computation, 28(127):679–693, July 1974. CODEN MCMPAF. ISSN 0025-5718 (paper), 1088-6842 (electronic). URL http:

//www.math.utah.edu/pub/tex/bib/gvl.bib;   http://www.
math.utah.edu/pub/tex/bib/mathcomp1970.bib.

Parlett:1974:BRH

[Par74c] Beresford N. Parlett. Book review: H. R. Schwarz, H. Rutishauser & E. Stiefel, translated by P. Hertelendy, Numerical Analysis of Symmetric Matrices, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1973, xi + 276 pp., 24 cm. Mathematics of Computation, 28(125): 328, January 1974. CODEN MCMPAF. ISSN 0025-5718 (print),

1088-6842 (electronic). URL https://www.jstor.org/stable/
2005845.

Parlett:1974:CFT

[Par74d] Beresford N. Parlett. Computation of functions of triangular matrices. Memorandum ERL-M481, Electronics Research Laboratory, College of Engineering, University of California, Berkeley, Berkeley, CA, USA, November 1974. 18 pp. URL

http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-
num-alg.bib;   http://www.math.utah.edu/pub/tex/bib/gvl.
bib.

Parlett:1976:RAE

[Par76a] B. N. Parlett. A recurrence among the elements of functions of triangular matrices. Linear Algebra and its Applications, 14(2): 117–121, ???? 1976. CODEN LAAPAW. ISSN 0024-3795 (print),

1873-1856 (electronic). URL http://www.sciencedirect.com/
science/article/pii/0024379576900185.

Parlett:1976:RES

[Par76b] Beresford N. Parlett. Roundoff error in the solution of finite element systems. Report ????, Electronics Research Laboratory, College of Engineering, University of California, Berkeley, Berkeley, CA, USA, 1976. 21 pp.

Parlett:1977:RES

[Par77a] Beresford Parlett. Roundoff error in the solution of finite element systems. In Bathe et al. [BOW77], pages 632–654. ISBN 0-262-02127-7. LCCN TA347.F5 F67; TA347.F5 F67.

Parlett:1977:PSD

[Par77b] Beresford N. Parlett. A program to swap diagonal blocks. Memorandum UCB/ERL M77/66, Electronics Research Laboratory, College of Engineering, University of California, Berkeley, Berkeley, CA, USA, November 3, 1977. 30 pp.

Parlett:1977:PNA

[Par77c] Beresford N. Parlett. Progress in numerical analysis. Memorandum UCB/ERL M77/26, Electronics Research Laboratory, College of Engineering, University of California, Berkeley, Berkeley, CA, USA, April 13, 1977. 30 pp.

Parlett:1978:PNA

[Par78] Beresford N. Parlett. Progress in numerical analysis. SIAM Review, 20(3):443–456, 1978. CODEN SIREAD. ISSN 0036-1445 (print),

1095-7200 (electronic). URL http://www.math.utah.edu/pub/
bibnet/subjects/acc-stab-num-alg.bib.

Parlett:1979:BRH

[Par79] Beresford N. Parlett. Book review: Herman H. Goldstine, A history of numerical analysis from the 16th through the 19th century. Studies in the History of Mathematics and Physical Sciences 2, Springer-Verlag, New York, Heidelberg, Berlin, 1977, xiv + 348 pp., $24.80. Bulletin of the American Mathematical Society (new series), 1(2):388–390, ???? 1979. CODEN BAMOAD. ISSN 0273-0979 (print), 1088-9485 (electronic). URL http://

projecteuclid.org/euclid.bams/1183544086.

Parlett:1980:HSK

[Par80a] B. N. Parlett. How to solve (K − λM)z = 0 for large K and M. In Absi [Abs80], pages 97–106. ISBN 2-04-012165-X (vol. 1), 2-04-012194-3 (vol. 2). LCCN TA329 .C64 1980; TA329 .C64 1980.

Parlett:1980:NLL

[Par80b] B. N. Parlett. A new look at the Lanczos algorithm for solving symmetric systems of linear equations. Linear Algebra and its Applications, 29:323–346, 1980. CODEN LAAPAW.

ISSN 0024-3795 (print), 1873-1856 (electronic). URL http:

//www.math.utah.edu/pub/tex/bib/gvl.bib;   http://www.
math.utah.edu/pub/tex/bib/linala1980.bib.

Parlett:1980:SEP

[Par80c] Beresford N. Parlett. The Symmetric Eigenvalue Problem. Series in Computational Mathematics. Prentice-Hall, Upper Saddle River, NJ 07458, USA, 1980. ISBN 0-13-880047-2. xix + 348 pp. LCCN QA188 .P3. Prentice-Hall Series in Computational Mathematics.

Parlett:1981:BRBb

[Par81a] B. N. Parlett. Book review: LINPACK Users’ Guide (J. J. Dongarra, J. R. Bunch, C. B. Moler and G. W. Stewart). SIAM Review, 23(1):126–128, ???? 1981. CODEN SIREAD. ISSN 0036-1445 (print), 1095-7200 (electronic).

Parlett:1981:PNA

[Par81b] Beresford Parlett. Progress in numerical analysis. Yingyong Shuxue yu Jisuan Shuxue, 3:1–10, 1981. Translated from the English by Wu Mu.

Parlett:1981:ACT

[Par81c] Beresford N. Parlett. Analytic complexity theory and the solution of AX = b. Technical Report PAM-40, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, June 1981.

Parlett:1981:HSK

[Par81d] Beresford N. Parlett. How to solve (K −λM)z = 0 for large K and M. Technical Report PAM-39, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, June 1981.

Parlett:1982:TMS

[Par82a] B. N. Parlett. Two monitoring schemes for the Lanczos algorithm. In Glowinski and Lions [GL82], pages x + 668. ISBN 0-444-86450-4. LCCN QA297 .E53 1981.

Parlett:1982:WFT

[Par82b]  B. N. Parlett.  Winograd’s Fourier transform via circu-

lants. Linear Algebra and its Applications, 45(??):137–155, 1982. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856

(electronic). URL http://www.math.utah.edu/pub/bibnet/
subjects/acc-stab-num-alg.bib;   http://www.math.utah.
edu/pub/tex/bib/linala1980.bib.

Parlett:1983:SPS

[Par83a] Beresford N. Parlett. Simmetrichnaya problema sobstvennykh znachenii. Chislennye metody (Russian) [The symmetric eigenvalue problem. Numerical methods]. Editorial Mir, Moscow, USSR, 1983. 384 pp. Translated from the English by Kh. D. Ikranov and Yu. A. Kuznetsov.

Parlett:1983:SSE

[Par83b] Beresford N. Parlett. The software scene in the extraction of eigenvalues from sparse matrices. Technical Report PAM-132, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, March 1983.

Parlett:1984:SSE

[Par84] B. N. Parlett. The software scene in the extraction of eigenvalues from sparse matrices. SIAM Journal on Scientific and Statistical Computing, 5(3):590–604, September 1984. CO-DEN SIJCD4. ISSN 0196-5204. URL http://www.math.utah.

edu/pub/bibnet/subjects/acc-stab-num-alg.bib;   http:/
/www.math.utah.edu/pub/tex/bib/fortran2.bib;   http://
www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib.

Parlett:1987:CJH

[Par87a] Beresford N. Parlett. A contribution of J. H. Wilkinson to numerical analysis. Technical Report PAM-372, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, April 1987.

Parlett:1987:MLA

[Par87b] Beresford N. Parlett. Misconvergence in the Lanczos algorithm. Technical Report PAM-404, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, December 1987.

Parlett:1987:SAE

[Par87c] Beresford N. Parlett. The state-of-the-art in extracting eigenvalues and eigenvectors in structural mechanics. Technical Report PAM-373, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, April 1987.

Parlett:1989:SBI

[Par89] Beresford N. Parlett. Some basic information on informationbased complexity theory. Technical Report PAM-460, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, July 1989.

Parlett:1990:CJH

[Par90a] Beresford N. Parlett. The contribution of J. H. Wilkinson to numerical analysis. In Nash [Nas90], pages 17–30. ISBN 0-201-50814-

1. LCCN QA76.17 .H59 1990. URL http://www.math.utah.edu/
pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;   http:/
/www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.
bib.

Parlett:1990:MLA

[Par90b] Beresford N. Parlett. Misconvergence in the Lanczos algorithm. In Cox and Hammarling [CH90], pages 7–24. ISBN 0-19-853564-3. LCCN QA297 .R435 1990. US$75.00. URL

http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-
num-alg.bib;   http://www.math.utah.edu/pub/tex/bib/numana1990.

bib. Based on papers from a conference in honour of the late James Hardy Wilkinson (died Sunday 5th October 1986) held at National Physical Laboratory, Teddington, Middlesex, UK, 8th–10th July 1987.

Parlett:1990:RTF

[Par90c] Beresford N. Parlett. Reduction to tridiagonal form and minimal realizations. Technical Report PAM-486, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, January 1990.

Parlett:1991:SMP

[Par91] Beresford N. Parlett. Symmetric matrix pencils. Journal of Computational and Applied Mathematics, 38(1–3):373–385, December 23, 1991. CODEN JCAMDI. ISSN 0377-0427 (print),

1879-1778 (electronic). URL http://www.sciencedirect.com/
science/article/pii/037704279190183K. Proceedings of the

International Symposium on Computational Mathematics (Matsuyama, 1990).

Parlett:1992:RTF

[Par92a] Beresford N. Parlett. Reduction to tridiagonal form and minimal realizations. SIAM Journal on Matrix Analysis and Applications, 13(2):567–593, April 1992. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic). URL http://www.math.utah.

edu/pub/bibnet/subjects/acc-stab-num-alg.bib;   http:/
/www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib.

Parlett:1992:RMS

[Par92b] Beresford N. Parlett. The rewards for maintaining semiorthogonality among Lanczos vectors. Journal of Numerical linear algebra with applications, 1(2):243–267, 1992. CODEN NLAAEM.

ISSN 0129-3281. URL http://www.math.utah.edu/pub/tex/
bib/numlinaa.bib.

Parlett:1992:SBI

[Par92c] Beresford N. Parlett. Some basic information on information-based complexity theory. Bulletin of the American Mathematical Society (new series), 26(1):3–27, 1992. CODEN BAMOAD. ISSN 0273-0979 (print), 1088-9485 (electronic). URL http://www.math.

utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib.

Parlett:1994:DWF

[Par94] Beresford N. Parlett. Do we fully understand the symmetric Lanczos algorithm yet? In Brown et al. [BCEP94], pages 93–107. ISBN 0-89871-339-0. LCCN QC19.2 .C67 1993. URL http://www.math.

utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib.

Parlett:1995:NA

[Par95] Beresford N. Parlett. The new qd algorithms. Acta Numerica, 4: 459–491, 1995. CODEN ANUMFU. ISBN 0-521-48255-0. ISSN 0962-4929 (print), 1474-0508 (electronic).

Parlett:1996:IST

[Par96a] B. N. Parlett. Invariant subspaces for tightly clustered eigenvalues of tridiagonals. BIT Numerical Mathematics, 36(3):542– 562, September 1996. CODEN BITTEL, NBITAB. ISSN 0006-3835 (print), 1572-9125 (electronic). URL http://www.

mai.liu.se/BIT/contents/bit36.html;   http://www.math.
utah.edu/pub/tex/bib/bit.bib. International Linear Algebra

Year (Toulouse, 1995).

Parlett:1996:OEG

[Par96b] B. N. Parlett. Orthogonal eigenvectors without Gram–Schmidt. In Watson and Griffiths [WG96], pages 140–153. ISBN 0-582-27633-0 (paperback). ISSN 0269-3674. LCCN QA297.N854 1996. Proceedings of the 16th Dundee Biennial Conference on Numerical Analysis, University of Dundee, June 27–30, 1995.

Parlett:1996:COE

[Par96c] Beresford N. Parlett. The construction of orthogonal eigenvectors for tight clusters by use of submatrices. Technical Report PAM-664, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, January 1996.

Parlett:1996:WHM

[Par96d] Beresford N. Parlett. What Hadamard missed. Technical Report PAM-671, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, March 1996.

Parlett:1997:NVP

[Par97] Beresford N. Parlett. New versions of qd for products of bidiagonals. In Buhmann et al. [BIP97], pages 183–200. ISBN 0-521-58190-7 (hardback). LCCN QA221 .A655 1997.

Parlett:1998:SSP

[Par98a] Beresford N. Parlett. Spectral sensitivity of products of bidiagonals. Linear Algebra and its Applications, 275/276(1–3):417–431, May 15, 1998. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-

1856 (electronic). URL http://www.elsevier.com/cas/tree/
store/laa/sub/1998/275-276/1-3/6055.pdf;   http://www.
elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/
browse.cgi?year=1998&volume=275-276&issue=1-3&aid=6055;
 http://www.math.utah.edu/pub/tex/bib/linala1990.bib. Pro-

ceedings of the Sixth Conference of the International Linear Algebra Society (Chemnitz, 1996).

Parlett:1998:SEP

[Par98b] Beresford N. Parlett. The Symmetric Eigenvalue Problem, volume 20 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1998. ISBN 0-89871-402-8 (paperback), 1-61197-116-0 (e-book). xxiv + 398 pp. LCCN QA188 .P37 1998. URL http://www.

loc.gov/catdir/enhancements/fy0708/97040623-d.html. Cor-

rected reprint [Par80c].

Parlett:2000:A

[Par00a] Beresford N. Parlett. The QR algorithm. Computing in Science and Engineering, 2(1):38–42, January/February 2000. CODEN CSENFA. ISSN 1521-9615 (print), 1558-366X (elec-

tronic). URL http://dlib.computer.org/cs/books/cs2000/
pdf/c1038.pdf;   http://ieeexplore.ieee.org/stamp/stamp.
jsp?tp=&arnumber=814656;   http://www.computer.org/cse/
cs1999/c1038abs.htm;   http://www.math.utah.edu/pub/tex/
bib/computscieng.bib.

Parlett:2000:TR

[Par00b] Beresford N. Parlett. For tridiagonals T replace T with LDL^{t}. Journal of Computational and Applied Mathematics, 123(1– 2):117–130, November 1, 2000. CODEN JCAMDI. ISSN 0377-0427 (print), 1879-1778 (electronic). URL http://www.

sciencedirect.com/science/article/pii/S0377042700003940.

Numerical analysis 2000, Vol. III. Linear algebra.

Parlett:2000:PSP

[Par00c] Beresford N. Parlett. Problems and solutions: Problems: 10839. American Mathematical Monthly, 107(10):950, 2000. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Parlett:2002:MDD

[Par02a] Beresford N. Parlett. The (matrix) discriminant as a determinant. Linear Algebra and its Applications, 355(1–3):85–101, November 1, 2002. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-

1856 (electronic). URL http://www.elsevier.nl/gej-ng/10/
30/19/201/27/33/abstract.html;   http://www.math.utah.
edu/pub/tex/bib/linala2000.bib.

Parlett:2002:QA

[Par02b] Beresford N. Parlett. The QR algorithm. World-Wide Web doc-

ument, April 22, 2002. URL http://www.cs.berkeley.edu/~
wkahan/Math128/Parlett.pdf;   http://www.math.utah.edu/
pub/bibnet/authors/k/kahan-william-m.bib. Lecture notes for

Math 128.

Parlett:2003:PEF

[Par03a] Beresford N. Parlett. Perturbation of eigenpairs of factored symmetric tridiagonal matrices. Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics, 3(2):207–223, 2003. ISSN 1615-3375 (print), 1615-3383 (electronic).

Parlett:2003:SDF

[Par03b] Beresford N. Parlett. The spectral diameter as a function of the diagonal entries. Numerical Linear Algebra with Applications, 10 (7):595–602, October/November 2003. CODEN NLAAEM. ISSN 1070-5325 (print), 1099-1506 (electronic). URL http://www.math.

utah.edu/pub/tex/bib/numlinaa.bib. Dedicated to the 70th

birthday of Ivo Marek.

Parlett:2005:BMD

[Par05] Beresford N. Parlett. A bidiagonal matrix determines its hyperbolic SVD to varied relative accuracy. SIAM Journal on Matrix Analysis and Applications, 26(4):1022–1057, 2005. CODEN SJ-MAEL. ISSN 0895-4798 (print), 1095-7162 (electronic).

Parlett:2007:WHM

[Par07] Beresford N. Parlett. What Hadamard missed. Internat. J. Appl. Sci. Comput., 14(3):116–136, 2007. ISSN 1089-0025.

Parlett:2008:RDE

[Par08] Beresford N. Parlett. Recollections (designed to entertain or enlighten). Web document, March 30, 2008. URL http://math. berkeley.edu/bascd08. The Bay Area Scientific Computing Day, BASCD08, honoring Profs. Kahan and Parlett, 29–30 March, 2008.

Parlett:2009:RCG

[Par09a] Beresford N. Parlett. A result complementary to Gersgorin’s Circle Theorem. Linear Algebra and its Applications, 431(1-2):20–27, 2009. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (electronic).

Parlett:2009:RFM

[Par09b] Beresford N. Parlett. Review of Functions of Matrices: Theory and Computation, Nicholas J. Higham. SIAM, Philadelphia, PA (2008), xx + 425 pp. Linear Algebra and its Applications, 430(11– 12):3139–3140, June 1, 2009. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (electronic).

Parlett:2010:BRB

[Par10] Beresford Parlett. Book review: The matrix eigenvalue problem: GR and Krylov subspace methods [book review of MR2383888]; Numerical methods for general and structured eigenvalue problems [book review of MR2164298]. SIAM Review, 52(4):771–774, ???? 2010. CODEN SIREAD. ISSN 0036-1445 (print), 1095-7200 (electronic).

Parlett:2006:AOM

[PB06] B. N. Parlett and E. Barszcz. Another orthogonal matrix. Linear Algebra and its Applications, 417(2-3):342–346, 2006. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (electronic).

Parlett:1988:UII

[PC88] Beresford N. Parlett and H. C. Chen. Use of an indefinite inner product for computing damped natural modes. Technical Report PAM-435, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, November 1988.

Parlett:1990:LAI

[PC90a] B. N. Parlett and H. C. Chen. The Lanczos algorithm with indefinite inner product. In Kaashoek et al. [KvSR90], pages 393–400. ISBN 0-8176-3469-X (vol 1), 0-8176-3470-3 (vol. 2), 0-8176-3471-1 (vol. 3), 0-8176-3468-1 (set). LCCN QA402 .P766 1989.

Parlett:1990:UIP

[PC90b] B. N. Parlett and H. C. Chen. Use of indefinite pencils for computing damped natural modes. Linear Algebra and its Applications, 140(??):53–88, 1990. CODEN LAAPAW. ISSN 0024-3795 (print),

1873-1856 (electronic). URL http://www.math.utah.edu/pub/
tex/bib/linala1990.bib.

Parlett:1997:FSW

[PD97] Beresford N. Parlett and Inderjit S. Dhillon. Fernando’s solution to Wilkinson’s problem: An application of double factorization. Linear Algebra and its Applications, 267(1–3):247– 279, December 1997. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (electronic). URL http://www.cs.utexas.

edu/users/inderjit/public_papers/pdonfer.pdf;   http:/
/www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/
browse.cgi?year=1997&volume=267&issue=1-3&aid=9700022;
 http://www.math.utah.edu/pub/tex/bib/linala1990.bib.

Parlett:2000:RRR

[PD00] Beresford N. Parlett and Inderjit S. Dhillon. Relatively robust representations of symmetric tridiagonals. Linear Algebra and its Applications, 309(1–3):121–151, April 15, 2000. CO-DEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (elec-

tronic).  URL http://www.elsevier.nl/gej-ng/10/30/19/
126/25/33/abstract.html;   http://www.elsevier.nl/gej-
ng/10/30/19/126/25/33/article.pdf;   http://www.math.utah.
edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;   http:
//www.math.utah.edu/pub/tex/bib/linala2000.bib.

Parlett:2016:IEP

[PDF16] Beresford Parlett, Froilán M. Dopico, and Carla Ferreira. The inverse eigenvector problem for real tridiagonal matrices. SIAM Journal on Matrix Analysis and Applications, 37(2):577–597, ???? 2016. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic).

Parlett:1975:PCR

[PF75] Beresford N. Parlett and R. Feldman. A program to compute the real Schur form of a real square matrix. Memorandum ERL-M526, Electronics Research Laboratory, College of Engineering, University of California, Berkeley, Berkeley, CA, USA, 1975. 28 pp.

Parlett:1994:PDQ

[PF94a] Beresford N. Parlett and K. Vince Fernando. Parallel differential qd for singular vectors. In Natori and Nodera [NN94], pages 242– 250. ISBN ???? LCCN ????

Parlett:1994:SVD

[PF94b] Beresford N. Parlett and K. Vince Fernando. Singular vectors via differential qd. In Lewis [Lew94], pages 161–165. ISBN 0-89871-336-6. LCCN QA184.S58 1994.

Parlett:1995:SVD

[PF95] Beresford N. Parlett and K. Vince Fernando. Singular vectors via differential qd. In Bailey et al. [BBG^{+}95], pages 564–568. ISBN 0-89871-344-7. LCCN QA76.58.S55 1995.

Parlett:1978:NPG

[PH78] B. N. Parlett and W. Hoffman. New proof of global convergence for tridiagonal QL algorithm. SIAM Review, 20(3):632, ???? 1978. CODEN SIREAD. ISSN 0036-1445 (print), 1095-7200 (electronic).

Parlett:1991:IMR

[PH91] Beresford N. Parlett and Wee-Liang Heng. Implementation of minimal representation in 2D Ising model calculations. Technical Report PAM-550, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, May 1991. Longer version (60 pages)(to be published) of #549.

Parlett:1992:MMR

[PH92] Beresford N. Parlett and Wee-Liang Heng. The method of minimal representations in 2D Ising model calculations. Technical Report PAM-549, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, May 1992. Abbreviated version (14 pages) of #550.

Parlett:1994:MMR

[PH94] Beresford N. Parlett and Wee-Liang Heng. The method of minimal representations in 2D Ising model calculations. Journal of computational physics, 114(2):257–264, October 1994. CO-DEN JCTPAH. ISSN 0021-9991 (print), 1090-2716 (electronic).

URL http://www.sciencedirect.com/science/article/pii/
S0021999184711648.

Parlett:1996:FRP

[PH96] B. N. Parlett and J. He. Frequency response plots: New approaches. Zeitschrift für Angewandte Mathematik und Mechanik, 76(Supplement 3):78–80, 1996. CODEN ZAMMAX. ISSN 0044-2267 (print), 1521-4001 (electronic).

Parlett:1997:NMR

[PH97] Beresford N. Parlett and Jianxun He. Nearly minimal reduced order systems. In Proceedings of the 36th IEEE Conference on Decision and Control, 1997, volume 4, pages 3867–3872. IEEE Computer Society Press, 1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA, 1997. URL http://ieeexplore.ieee.

org/stamp/stamp.jsp?tp=&arnumber=652465.

Parlett:1969:CPA

[PK69] B. N. Parlett and W. Kahan. On the convergence of a practical QR algorithm. (With discussion). In Morrell [Mor69], pages 114–118. ISBN 0-7204-2032-6. LCCN QA76 .I578.

Parlett:2002:LEP

[PKS02] Beresford N. Parlett, Olaf Krafft, and Martin Schaefer. The largest eigenvalue of a positive definite symmetric matrix: 10839. American Mathematical Monthly, 109(10):922–923, December 2002. CO-DEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

URL http://www.jstor.org/stable/3072468.

Parlett:1981:MSD

[PL81] Beresford N. Parlett and T. L. Landis. Methods for scaling to doubly stochastic form. Technical Report PAM-44, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, June 1981.

Parlett:1982:MSD

[PL82] B. N. Parlett and T. L. Landis. Methods for scaling to doubly stochastic form. Linear Algebra and its Applications, 48(??):53– 79, 1982. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856

(electronic). URL http://www.math.utah.edu/pub/bibnet/
subjects/acc-stab-num-alg.bib;   http://www.math.utah.
edu/pub/tex/bib/linala1980.bib.

Parlett:1991:QFI

[PL91] Beresford N. Parlett and Jian Le. QR; its forward instability and failure to converge. In Albrecht [Alb91], pages 177–189. ISBN 3-7643-2575-5.

Parlett:1992:MES

[PL92] Beresford N. Parlett and Tzon-Tzer Lu. Minimum eigenvalue separation. Technical Report PAM-560, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, July 1992.

Parlett:1993:FIT

[PL93] Beresford N. Parlett and Jian Le. Forward instability of tridiagonal QR. SIAM Journal on Matrix Analysis and Applications, 14 (1):279–316, January 1993. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic). URL http://www.math.utah.

edu/pub/bibnet/subjects/acc-stab-num-alg.bib;   http:/
/www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib.

Parlett:2000:IAP

[PM00] Beresford N. Parlett and Osni A. Marques. An implementation of the dqds algorithm (positive case). Linear Algebra and its Applications, 309(1–3):217–259, April 15, 2000. CO-DEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (elec-

tronic).  URL http://www.elsevier.nl/gej-ng/10/30/19/
126/25/37/abstract.html;   http://www.elsevier.nl/gej-
ng/10/30/19/126/25/37/article.pdf;   http://www.math.utah.
edu/pub/tex/bib/lawn.bib;   http://www.math.utah.edu/pub/

tex/bib/linala2000.bib. See original LAPACK Working note in [PM02].

Parlett:2002:IDA

[PM02] Beresford N. Parlett and Osni A. Marques. An implementation of the dqds algorithm positive case. LAPACK Working Note 155, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, August 2002.

URL http://www.math.utah.edu/pub/tex/bib/lawn.bib;
http://www.netlib.org/lapack/lawns/lawn155.ps;   http:
//www.netlib.org/lapack/lawnspdf/lawn155.pdf.  LBNL-

43726, UT-CS-02-475, August 2002. Published in [?].

Parlett:1985:DAA

[PN85] Beresford N. Parlett and K. C. Ng. Development of an accurate algorithm for exp(Bt). Technical Report PAM-294, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, August 1985.

Parlett:1986:ACM

[PN86] B. N. Parlett and K. C. Ng. Accurate computation of the matrix exponential. In Glowinski and Lions [GL86], pages 107–116. ISBN 0-444-70059-5. LCCN TA345.

Parlett:1987:PSD

[PN87] Beresford N. Parlett and K. C. Ng. Programs to swap diagonal blocks. Technical Report PAM-381, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, June 1987.

Parlett:1982:AUE

[PNO82a] Beresford N. Parlett and B. Nour-Omid. An algorithm to update eigenvalues of a growing symmetric tridiagonal matrix. Technical Report PAM-104, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, October 1982.

Parlett:1982:EP

[PNO82b] Beresford N. Parlett and B. Nour-Omid. Element preconditioning. Technical Report PAM-103, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, October 1982.

Parlett:1983:URE

[PNO83] Beresford N. Parlett and B. Nour-Omid. The use of refined error bound when updating eigenvalues of tridiagonals. Technical Report PAM-175, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, September 1983.

Parlett:1985:URE

[PNO85] B. N. Parlett and B. Nour-Omid. The use of a refined error bound when updating eigenvalues of tridiagonals. Linear Algebra and its Applications, 68(??):179–219, 1985. CODEN LAA-PAW. ISSN 0024-3795 (print), 1873-1856 (electronic). URL http:

//www.math.utah.edu/pub/tex/bib/gvl.bib;   http://www.
math.utah.edu/pub/tex/bib/linala1980.bib.

Parlett:1989:TBB

[PNO89] Beresford N. Parlett and Bahram Nour-Omid. Towards a black box Lanczos program. Computer Physics Communications, 53 (1–3):169–179, May 1989. CODEN CPHCBZ. ISSN 0010-4655 (print), 1879-2944 (electronic). URL http://www.math.utah.

edu/pub/bibnet/subjects/acc-stab-num-alg.bib;   http:/
/www.sciencedirect.com/science/article/pii/0010465589901586.

Parlett:1985:ILA

[PNOJ85] B. Parlett, B. Nour-Omid, and J. Jatvig. Implementation of Lanczos algorithms on vector computers. In Numrich [Num85], pages 1–

18. ISBN 0-306-42013-9. LCCN QA76.5.S8944 1984a. URL http:/

/www.math.utah.edu/pub/tex/bib/ovr.bib. Proceedings of the

Supercomputer Applications Symposium cosponsored by the Purdue University Computing Center, the Purdue Center for Parallel and Vector Computing, and Control Data, held October 31– November 1, 1984, in West Lafayette, Indiana.

Parlett:1981:FSF

[PNOL81] Beresford N. Parlett, B. Nour-Omid, and M. R. Li. A fast solver free of fill-in for finite element problems. Technical Report PAM-42, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, June 1981.

Parlett:1988:HMS

[PNOL88] Beresford N. Parlett, B. Nour-Omid, and Zhishun A. Liu. How to maintain semi-orthogonality among Lanczos vectors. Technical Report PAM-420, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, July 1988.

Parlett:1984:ECM

[PNON84] Beresford N. Parlett, B. Nour-Omid, and J. Natvig. Effect of the CYBER 205 on methods for computing natural frequencies of structures. Technical Report PAM-218, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, April 1984.

Parlett:1987:CLC

[PNOR87] Beresford N. Parlett, B. Nour-Omid, and A. Raefsky. Comparison of Lanczos with conjugate gradient using element preconditioning. Technical Report PAM-363, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, February 1987.

Parlett:1973:GTP

[PP73] B. N. Parlett and W. G. Poole, Jr. A geometric theory for the QR, LU and power iterations. SIAM Journal on Numerical Analysis, 10(2):389–412, April 1973. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic). URL http:

//www.math.utah.edu/pub/tex/bib/gvl.bib;   http://www.
math.utah.edu/pub/tex/bib/siamjnumeranal.bib. Collection

of articles dedicated to the memory of George E. Forsythe.

Paige:1993:ASEa

[PPV93] C. C. Paige, B. N. Parlett, and H. A. Van der Vorst. Approximate solutions and eigenvalue bounds from Krylov subspaces. Technical Report PAM-579, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, February

1993. URL http://www.math.utah.edu/pub/bibnet/authors/
v/vandervorst-henk-a.bib.

Paige:1995:ASE

[PPv95] Chris C. Paige, Beresford N. Parlett, and Henk A. van der Vorst. Approximate solutions and eigenvalue bounds from Krylov subspaces. Numerical Linear Algebra with Applications, 2(2):115– 133, 1995. CODEN NLAAEM. ISSN 1070-5325 (print), 1099-

1506 (electronic). URL http://www.math.utah.edu/pub/tex/
bib/numlinaa.bib.

Parlett:1969:BMC

[PR69] B. N. Parlett and C. Reinsch. Balancing a matrix for calculation of eigenvalues and eigenvectors. Numerische Mathematik, 13:293– 304, 1969. CODEN NUMMA7. ISSN 0029-599X (print), 0945-3245

(electronic). URL http://www.math.utah.edu/pub/bibnet/
subjects/acc-stab-num-alg.bib;   http://www.math.utah.
edu/pub/tex/bib/gvl.bib;   http://www.math.utah.edu/pub/

tex/bib/nummath.bib. Also in [WR71, pp. 315–326].

Parlett:1970:SSL

[PR70] B. Parlett and J. K. Reid. On the solution of a system of linear equations whose matrix is symmetric but not definite. BIT (Nordisk tidskrift for informationsbehandling), 10(3):386–397, 1970. CODEN BITTEL, NBITAB. ISSN 0006-3835 (print), 1572-

9125 (electronic). URL http://www.math.utah.edu/pub/tex/
bib/bit.bib;   http://www.math.utah.edu/pub/tex/bib/gvl.
bib.

Parlett:1981:TPL

[PR81] B. N. Parlett and J. K. Reid. Tracking the progress of the Lanczos algorithm for large symmetric eigenproblems. IMA Journal of Numerical Analysis, 1(2):135–155, 1981. CODEN IJ-NADH. ISSN 0272-4979 (print), 1464-3642 (electronic). URL

http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-
num-alg.bib;   http://www.math.utah.edu/pub/tex/bib/gvl.
bib;   http://www.math.utah.edu/pub/tex/bib/imajnumeranal.
bib.

Parlett:1977:LAI

[PS77] B. N. Parlett and D. S. Scott. The Lanczos algorithm with implicit deflation. Memorandum UCB/ERL M77/70, Electronics Research Laboratory, College of Engineering, University of California, Berkeley, Berkeley, CA, USA, December 2, 1977. 29 pp.

Parlett:1979:LAS

[PS79] B. N. Parlett and D. S. Scott. The Lánczos algorithm with selective orthogonalization. Mathematics of Computation, 33(145):217–238, January 1979. CODEN MCMPAF. ISSN 0025-5718 (paper), 1088-6842 (electronic). URL http:

//www.math.utah.edu/pub/tex/bib/gvl.bib;   http://www.
math.utah.edu/pub/tex/bib/mathcomp1970.bib.

Parlett:1985:CSI

[PS85] Beresford N. Parlett and Y. Saad. Complex shift and invert strategies for real matrices. Research report RR-424, Department of Computer Science, Yale University, New Haven, CT, USA, 1985. 17 pp.

Parlett:1987:CSI

[PS87a] Beresford N. Parlett and Youcef Saad. Complex shift and invert strategies for real matrices. Linear Algebra and its Applications, 88/89(??):575–595, 1987. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (electronic). URL http://www.math.

utah.edu/pub/bibnet/authors/s/saad-yousef.bib;   http:
//www.math.utah.edu/pub/tex/bib/linala1980.bib.

Parlett:1987:BRT

[PS87b] Beresford N. Parlett and Robert Schreiber. Block reflectors: theory and computation. Technical Report PAM-378, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, May 1987.

Parlett:2008:MPR

[PS08] Beresford Parlett and Gilbert Strang. Matrices with prescribed Ritz values. Linear Algebra and its Applications, 428(7):1725–1739, 2008. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (electronic).

Parlett:1982:ELE

[PSS82] B. N. Parlett, H. Simon, and L. M. Stringer. On estimating the largest eigenvalue with the Lánczos algorithm. Mathematics of Computation, 38(157):153–165, January 1982. CODEN MCMPAF. ISSN 0025-5718 (paper), 1088-6842

(electronic). URL http://www.math.utah.edu/pub/bibnet/
subjects/acc-stab-num-alg.bib;   http://www.math.utah.
edu/pub/tex/bib/gvl.bib;   http://www.math.utah.edu/pub/
tex/bib/mathcomp1980.bib.

Parlett:1981:BRBa

[PT81a] B. Parlett and R. Tolimieri. Book review: A Matrix Eigenvalue Problem (G. Efroymson, A. Steger and S. Steinberg). SIAM Review, 23(1):105, ???? 1981. CODEN SIREAD. ISSN 0036-1445 (print), 1095-7200 (electronic).

Parlett:1981:LAL

[PT81b] Beresford N. Parlett and D. Taylor. A look-ahead Lanczos algorithm for unsymmetric matrices. Technical Report PAM-43, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, June 1981.

Parlett:1984:LAL

[PTL84] B. N. Parlett, D. R. Taylor, and Z. S. Liu. The look ahead Lánczos algorithm for large unsymmetric eigenproblems. In Glowinski and Lions [GL84], pages 87–96. ISBN 0-444-87597-2. LCCN QA297 .I57 1983.

Parlett:1985:LAL

[PTL85] Beresford N. Parlett, Derek R. Taylor, and Zhishun A. Liu. A look-ahead Lánczos algorithm for unsymmetric matrices. Mathematics of Computation, 44(169):105–124, January 1985. CODEN MCMPAF. ISSN 0025-5718 (paper), 1088-6842 (electronic). URL

http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib.

Parlett:2004:HMA

[PV04] Beresford N. Parlett and Christof Vömel. How the MRRR algorithm can fail on tight eigenvalue clusters. LAPACK Working Note 163, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, December

2004. 15 pp. URL http://www.eecs.berkeley.edu/Pubs/
TechRpts/2004/CSD-04-1367.pdf;   http://www.math.utah.
edu/pub/tex/bib/lawn.bib;   http://www.netlib.org/lapack/
lawns/lawn163.ps;   http://www.netlib.org/lapack/lawnspdf/

lawn163.pdf. UT-CS-04-542, December, 2004.

Parlett:2009:SGM

[PV09] Beresford N. Parlett and Christof Vömel. The spectrum of a glued matrix. SIAM Journal on Matrix Analysis and Applications, 31 (1):114–132, 2009. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic).

Parlett:1975:ICC

[PW75] B. N. Parlett and Y. Wang. The influence of the compiler on the cost of mathematical software—in particular on the cost of triangular factorization. ACM Transactions on Mathematical Software, 1(1):35–46, March 1975. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic).

Parlett:1977:ICC

[PW77] B. N. Parlett and Y. Wang. The influence of the compiler on the cost of mathematical software—in particular on the cost of triangular factorization. ACM Transactions on Mathematical Software, 1:35–46, 1977. CODEN ACMSCU. ISSN 0098-3500 (print),

1557-7295 (electronic). URL http://www.math.utah.edu/pub/
bibnet/subjects/acc-stab-num-alg.bib.

Parlett:1984:EMS

[PW84] B. N. Parlett and W. D. Wu. Eigenvector matrices of symmetric tridiagonals. Numerische Mathematik, 44(1):103–110, June 1984. CODEN NUMMA7. ISSN 0029-599X (print), 0945-3245

(electronic). URL http://www.math.utah.edu/pub/tex/bib/
nummath.bib.

Parlett:1983:EMS

[PWW83] Beresford N. Parlett, H. Wu, and W. D. Wu. Eigenvector matrices of symmetric tridiagonals. Technical Report PAM-174, Center for Pure and Applied Mathematics, University of California, Berkeley, Berkeley, CA, USA, August 1983.

Rust:1966:SAC

[RBS66] B. Rust, W. R. Burrus, and C. Schneeberger. A simple algorithm for computing the generalized inverse of a matrix. Communications of the ACM, 9(5):381–385, 387, May 1966. CODEN CACMA2. ISSN 0001-0782 (print), 1557-7317 (electronic). URL http://www.

math.utah.edu/pub/tex/bib/cacm1960.bib.

Rice:1979:NCN

[RGO^{+}79] J. R. Rice, C. W. Gear, J. Ortega, B. Parlett, M. Schultz, L. F. Shampine, P. Wolfe, and J. F. Traub. Numerical computation: its nature and research directions. ACM SIGNUM Newsletter, 14 (3S (Special issue)):1–48, February 1979. CODEN SNEWD6. ISSN 0163-5778 (print), 1558-0237 (electronic). URL http://www.math.

utah.edu/pub/tex/bib/signum.bib.

Reichel:1993:NLA

[RRV93] Lothar Reichel, Arden Ruttan, and Richard S. Varga, editors. Numerical linear algebra: proceedings of the Conference in Numerical Linear Algebra and Scientific Computation, Kent (Ohio), USA, March 13–14, 1992. Walter de Gruyter, Berlin, Germany, 1993. ISBN 3-11-013784-4. LCCN QA184.C655 1993.

Renegar:1996:MNA

[RSS96] James Renegar, Michael Shub, and Steve Smale, editors. The mathematics of numerical analysis: 1995 AMS–SIAM Summer Seminar in Applied Mathematics, July 17–August 11, 1995, Park City, Utah, volume 32 of Lectures in Applied Mathematics — American Mathematical Society. American Mathematical Society, Providence, RI, USA, 1996. ISBN 0-8218-0530-4. ISSN 0075-8485. LCCN QA297 .A57 1995.

Ralston:1967:MMD

[RW67] Anthony Ralston and Herbert S. Wilf, editors. Mathematical Methods for Digital Computers, volume II. Wiley, New York, NY, USA; London, UK; Sydney, Australia, 1967. ISBN 0-471-70686-8 (vol. 1), 0-471-70689-2 (vol. 2), 0-471-70690-6 (vol. 3). LCCN ????

Shub:1996:PDD

[SCI^{+}96] M. Shub, Alexandre Chorin, Arieh Iserles, Beresford Parlett, Steve Smale, and Shmuel Winograd. Panel discussion: Does numerical analysis need a model of computation? In Renegar et al. [RSS96], pages 1–18. ISBN 0-8218-0530-4. ISSN 0075-8485. LCCN

QA297 .A57 1995. URL http://www.math.utah.edu/pub/tex/
bib/numana1990.bib.

Schreiber:1986:BRC

[SP86] Robert S. Schreiber and Beresford N. Parlett. Block reflectors: Computation and applications. In Glowinski and Lions [GL82], pages 71–79. ISBN 0-444-86450-4. LCCN QA297 .E53 1981.

Schreiber:1988:BRT

[SP88] Robert S. Schreiber and Beresford N. Parlett. Block reflectors: Theory and computation. SIAM Journal on Numerical Analysis, 25(1):189–205, February 1988. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic). URL http://www.math.

utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-
num-alg.bib;   http://www.math.utah.edu/pub/tex/bib/ovr.
bib;   http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.
bib.

Shomron:2009:LAM

[SP09] Noam Shomron and Beresford N. Parlett. Linear algebra meets Lie algebra: the Kostant–Wallach theory. Linear Algebra and its Applications, 431(10):1745–1767, 2009. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (electronic).

Schulman:2017:ACM

[SS17] Leonard J. Schulman and Alistair Sinclair. Analysis of a classical matrix preconditioning algorithm. Journal of the ACM, 64(2): 9:1–9:23, June 2017. CODEN JACOAH. ISSN 0004-5411 (print), 1557-735X (electronic).

Traub:1992:PIB

[TW92] J. F. Traub and H. Woźniakowski. Perspectives on informationbased complexity. Bulletin of the American Mathematical Society (new series), 26(1):29–52, 1992. CODEN BAMOAD. ISSN 0273-0979 (print), 1088-9485 (electronic). URL http://www.math.

utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib. Re-

ply to [Par92c].

Varah:1966:CPA

[Var66] J. M. Varah. Certification of Parlett’s ALGOL eigenvalue procedure Eig 3 (in Technical Notes and Short Papers). Mathematics of Computation, 20(95):437–438, July 1966. CODEN MCMPAF. ISSN 0025-5718 (paper), 1088-6842 (electronic). URL http://

www.math.utah.edu/pub/tex/bib/mathcomp1960.bib.

Vomel:2011:DLI

[VP11] Christof Vömel and Beresford N. Parlett. Detecting localization in an invariant subspace. SIAM Journal on Scientific Computing, 33(6):3447–3467, ???? 2011. CODEN SJOCE3. ISSN 1064-8275 (print), 1095-7197 (electronic). URL http://epubs.siam.org/

sisc/resource/1/sjoce3/v33/i6/p3447_s1.

Watson:1996:NA

[WG96] G. A. Watson and D. F. Griffiths, editors. Numerical analysis 1995, volume 344 of Pitman research notes in mathematics series. Longman Scientific and Technical, Harlow, Essex, UK, 1996. ISBN 0-582-27633-0 (paperback). ISSN 0269-3674. LCCN QA297.N854 1996. Proceedings of the 16th Dundee Biennial Conference on Numerical Analysis, University of Dundee, June 27–30, 1995.

Wilkinson:1971:LA

[WR71] James H. Wilkinson and Christian Reinsch, editors. Linear Algebra, volume II of Handbook for Automatic Computation, Editors: F. L. Bauer, A. S. Householder, F. W. J. Olver, H. Rutishauser, K. Samelson and E. Stiefel. Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 1971. ISBN 0-387-05414-6, 3-540-05414-6. viii + 439 pp. LCCN QA251 .W67.

Wang:2020:KPJ

[WW20] Yunjie Wang and Gang Wu. On the Kahan–Parlett–Jiang theorem — a globally optimal backward perturbation error for two-sided invariant subspaces. Linear Algebra and its Applications, 602(??):73– 92, October 1, 2020. CODEN LAAPAW. ISSN 0024-3795 (print),

1873-1856 (electronic). URL http://www.sciencedirect.com/
science/article/pii/S0024379520302342.

Zheng:2005:TLT

[ZPP05a] Xiaoqiang Zheng, Beresford N. Parlett, and Alex Pang. Topological lines in 3D tensor fields and discriminant Hessian factorization. IEEE Transactions on Visualization and Computer Graphics, 11 (4):395–407, July/August 2005. CODEN ITVGEA. ISSN 1077-2626 (print), 1941-0506 (electronic), 2160-9306.

Zheng:2005:TST

[ZPP05b] Xiaoqiang Zheng, Beresford N. Parlett, and Alex T. Pang. Topological structures of 3D tensor fields. In IEEE Visualization, 2005. VIS 05, pages 551–558. IEEE Computer Society Press, 1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA,

2005. URL http://ieeexplore.ieee.org/stamp/stamp.jsp?
tp=&arnumber=1532841.