A Bibliography of Publications by, and about, Wallace Givens

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: https://www.math.utah.edu/~beebe/

17 November 2023 Version 1.02

Abstract

This bibliography records publications of Wallace Givens.

Title word cross-reference

1024 [Giv68]. H [LZW^{+}18]. k [Kon02]. LU [Abd18, Mar18]. QR [CM99, FA17, GHL^{+}19, Gen75, GO95, HS86, HK06, Ips84, Kon02, SM02, SVTD19]. QZ [MM86, Mär87].

*36 [Ano93].

-algorithm [MM86]. -Algorithmus [MM86]. -Decomposition [SM02, SVTD19].

-matrices [LZW^{+}18]. -terminology [FC06].

1 [Hop97]. 163 [Cla81]. 1986 [CRTQ86].

3D [PW18].

539 [HH04, LHKK79]. 5425 [Mar67].

653 [HK87]. 663 [LN88].

830 [HH04].

abbreviation [Giv68]. adaptive [Del98]. ahead [ZHF95a, ZHF95b]. Algebra [DG82, Dod83, HK87, LHKK79, LN88, Giv51]. Algorithm [BG88, Cla81, MBM98, PW18, BKŻ16, BKŻ17, Del98, HB97, LCZ97, Mär87, Meg93, MAMB14, MCLM20, YJ01, ZQW14, ZHF95a, ZHF95b, dMdSK07, Cla81, DG82, Dod83, HK87, HH04, HH18, LHKK79, LN88, MM86]. Algorithms [CD94, PR87, Bor21, CRTQ86, HGP86, Kon02, PC99, PR89, SAMAN18]. Algorithmus [MM86]. Alternative [MC84, LLR^{+}90]. Analyses [GLN86b]. Analysis [Gen75, Del98, FC06, PW18]. Application [BKŻ16, Xie88]. applications [RASSI10]. Applied [HW79, JO03, JO05, KK78]. Approach [RTDL94, Abd18, Mar18]. approximation [LS17]. April [CRTQ86]. architectures [CRTQ86, CDR89, SVTD19, VKS^{+}15]. Argonne [Yoo05]. array [DS88, DS89]. Arrays [BI87, GV87, GS91].

B [Giv51]. Back [Cla81]. backward [HB97]. Bailey [Mar67]. band [LS17]. band-dominated [LS17]. Based [MBM98, SPC^{+}16, DV00, DV03, FA17, GHL^{+}19, HB97, LZW^{+}18, MAMB14, MCLM20, PC99, SVTD19, VKS^{+}15, dMdSK07]. Basic [HK87, DG82, Dod83, LHKK79, LN88]. Batcher [Meg93]. Bayesian [PJM^{+}21]. Bipartite [GLN84]. bK [Giv68]. BLAS [HK87, Hop97]. Blind [SAMAN18]. Book [BG64, Jon06]. bordered [Abd18, Mar18]. Bounds [Cau58]. Brenner [BG64]. Browne [Giv59].

cache [CM99]. cache- [CM99]. Calculation [Wil57]. Carefully [HH18]. Centre [CRTQ86]. Characteristic [Giv57, Giv54]. classical [Giv53]. co [RW61]. co-diagonalization [RW61]. Coarse [CD94]. Coarse-Grained [CD94]. Codiagonal [Wil57]. College [Giv51]. Column [CUM86, ZHF95a, ZHF95b]. Combining [FsH20, Sou09]. Compact [OB94]. compensated [Bor21]. complex [MAMB14, VG55, Xu88]. Complexity [CDR89]. composed [PW18]. Computation [Giv58a, Giv54].

Computational [Yoo05, Jon06].

Computations [Gen73, Giv58b, Döh89]. Computer [Yoo05, KKK83, RW61]. Computing [BDKM00, HH18, Hop97, BDKM02, Giv53, HS86, HK06, Kon02]. conducted [VG55]. Conference [Giv58b]. Connected [MBM98]. constellations [SAMAN18]. Construction [LZW^{+}18]. Coordinates [Giv36, Giv37b, Giv37a]. Corrigendum [Dod83]. Cyber [LN88].

Data [Cla81, HK87, SPC^{+}16].

Decomposition [CUM86, GL87, SM02, CM99, FA17, HK06, Kon02, SVTD19]. Decompositions [Gen75]. Dedication [GP91]. deductive [Ace11]. dense [CDMR86, CR88]. Determinants [Giv59]. determination [dMdSK07]. determine [Wu16]. Devices [GV87]. diagonal [ZQW14]. diagonalization [MAMB14, MCLM20, RW61, Sou09]. differentiation [Giv34]. Diophantine [Giv47]. Direct [RTDL94, VKS^{+}15]. Distributed [PR87, PR89, PZN96]. Division [GS91]. domains [VG55]. dominated [LS17]. Duane [Mar67].

E. [Giv51]. E1521 [HRH^{+}62, HM63]. E1522 [RP63]. E1523 [HT63]. E1524 [WW63]. E1525 [HRH^{+}62, HYG63]. E288 [CBK^{+}37, CB38, Cam38]. E289 [BB38]. E290 [KS38]. E291 [TB38]. E292 [MS38]. E293 [BGW38a, BC38, BGW38b, CBK^{+}37]. Editor [Giv68, RW62]. Edward [Giv59]. Efficient [SPC^{+}16, CM99, LS17, PC99, RW61]. efficiently [BDKM00, BDKM02]. eigenspace [Del98]. Eigenvalue [Joh61]. Eigenvalues [LLR^{+}90, Giv53, LZW^{+}18]. Eigenvectors [Wil57, Giv53]. Elementary [BB38, BGW38a, BC38, BGW38b, CBK^{+}37, CB38, Cam38, HRH^{+}62, HM63, HYG63, HT63, KS38, MS38, RP63, TB38, WW63]. eliminating [ZHF95a, ZHF95b]. eliminating-ahead [ZHF95a, ZHF95b]. elimination [HB97]. Emergence [Yoo05]. employing [dMdSK07]. Endmember [GHL^{+}19]. Energy [SPC^{+}16]. Energy-Efficient [SPC^{+}16]. Equations [MBM98, Giv47, HGP86, RASSI10]. EREW [HK06, Kon00]. Error [Cau58, Gen75, ZXLL17]. estimating [Xie88]. Euclidean [HH18]. Evaluation [Joh61]. extraction [GHL^{+}19].

F [BG64, Mar67]. F1 [DG82, LHKK79]. factor [OB94]. factorisation [GHL^{+}19]. Factorization [CD94, GO95, Giv40, PR87, BY09, CR88, CDR89, HS86, PDW02, PR89]. factorizations [CDMR86]. Fast [Bor21, GLJ^{+}91, Ips84, JO05, KK78, Rat82, Han73, HB97, Ji88, KKK83, MM86, Mär87, Xie88, Xu88, ZQW14]. Fault [MBM98]. Fault-Tolerant [MBM98]. Fields [Giv52]. filtering [Bla85]. filters [PW18]. finite [PW18]. Flow [SPC^{+}16]. Form [Giv58a, JO04]. forms [Ace11]. Fortran [HH18, Dod83, HK87, LN88, DG82, LHKK79]. FPGA [SM02]. France [CRTQ86]. Free [GS91, Dua88]. full [LZW^{+}18].

General [Giv58a, Kon00, Liu86]. generalization [BMY13]. Geof [Jon06]. geometrical [FC06]. Geometry [VG55]. given [LZW^{+}18, DS89]. Givens [Ano93, Jon06, Mar67, Poo93, Poo94, Abd18, Ace11, BY09, BI87, BW84, BG88, BMY13, BKŻ16, BKŻ17, BDKM00, BDKM02, Bla85, Bor21, Bro98, CM99, Cau58, CUM86, Cla81, CDMR86, CR88, CDR89, CD94, Del98, DV08, DV00, DV03, DS88, Döh88, Döh89, Döh91, Dua88, Duf74, FA17, FsH20, FC06, GHL^{+}19, GV87, Gen73, Gen75, GLJ^{+}91, GH80, GLN84, GLN86a, GLN86b, GL87, GO95, GP91, GS91, Ham74, Han73, HW79, HH04, HGP86, HS86, HK06, HB97, Hop97, HLP81, Ips84, JO03, JO04, JO05, Ji88, Joh61, Kon00, Kon02, KK78, KKK83, LLR^{+}90, LZW^{+}18, LCZ97, LS17, Liu86, MM86, Mär87, Mar18, Meg93, MAMB14, MCLM20, MC84, MBM98, OB94, Ost87, PC99, PDW02, PZN96, PW18, PR87, PR89, PJM^{+}21, RTDL94, Rat82]. Givens [RASSI10, RW61, RW62, SM02, SAMAN18, SPC^{+}16, SVTD19, Sou09, Ste97, Tan82, Tan83, VKS^{+}15, Wil57, Wu16, Xie88, Xu88, YJ01, YH09, Yub91, ZQW14, ZXLL17, ZHF95a, ZHF95b, dMdSK07]. Givens- [Mar18]. Givens-like [MCLM20]. Givens-rotation [Wu16]. Givens-Rotationen [MM86]. Givens-Weight [DV08]. GMRES [YH09]. Goes [GLJ^{+}91]. Going [Cla81]. GPS [dMdSK07]. GPU [VKS^{+}15]. Grained [CD94]. Graph [Ste97, GLN84, GLN86a]. Graph-Theoretic [Ste97]. Greedy [Kon02]. Greek [Ace11, FC06].

H [Jon06]. Hardware [SVTD19]. Hessenberg [JO04, JO05]. high [SAMAN18]. high-order [SAMAN18]. higher [MCLM20]. higher-order [MCLM20]. Hoeting [Jon06]. homogeneous [Giv47, KK78]. Householder [DV00, DV03, GL87, PR87, PR89, RW62, Tan82, Tan83, YJ01, ZXLL17]. HR [Ji88]. Huang [LCZ97]. hyperbolic [SAMAN18, Sou09]. hyperspectral [GHL^{+}19]. hypotenuse [Bor21].

ICA [Wu16]. II [GLN86a, PDW02]. III [GLN86b]. image [RASSI10]. imagery [GHL^{+}19]. Implementation [HH18, SM02, SPC^{+}16, ZHF95b, BKŻ17, KKK83, PDW02]. Implications [Ste97]. Implicit [GLN86a]. impulse [PW18]. Incomplete [PDW02, BY09, YH09]. Inference [PJM^{+}21]. Ingram [Mar67]. instruction [DS88, DS89]. Integrated [GV87]. integrators [DV00, DV03]. INTEL [HK87]. International [CRTQ86]. interpretation [FC06]. interruption [Ji88]. Introduction [Giv59]. iteration [Ji88].

J [BG64]. J. [GP91]. James [Ano93, Poo93, Poo94]. Jennifer [Jon06]. John [VG55]. joint [MAMB14, MCLM20, Sou09]. Jr [Ano93]. Jr. [Poo93, Poo94].

kernel [ZXLL17].

L [BG64]. Laboratory [Yoo05]. Lanczos [Wil57]. language [Ace11]. Large [Joh61, HLP81, Ost87, RASSI10, YH09]. learning [BKŻ16, BKŻ17]. Least [BI87, Bla85, Gen73, GS91, GH80, HLP81, OB94, Ost87, Tan82, Tan83, Xie88, YH09, dMdSK07]. Least-squares [Bla85, YH09, dMdSK07]. Letter [Giv68, RW62]. Level [Hop97, RW61]. like [MCLM20]. Linear [BI87, Cla81, DG82, Dod83, Giv36, HK87, LHKK79, LN88, MBM98, Abd18, GH80, Giv37b, Giv37a, Giv47, HGP86, Kon00, Mar18, PZN96, RASSI10]. Lorentz [Giv40]. LP [HW79]. Luminy [CRTQ86].

M [Giv51, Mar67]. machines [PZN96]. Manifold [PJM^{+}21]. Marcus [Mar67]. Marvin [Mar67]. Mathematical [HW79]. Mathematics [Giv62, Ace11]. Mathématiques [CRTQ86]. MATLAB [GLJ^{+}91]. Matrices [DV08, Joh61, Wil57, CDMR86, CR88, Duf74, Giv40, Giv53, JO04, JO05, LLR^{+}90, LZW^{+}18, Giv59]. Matrix [GV87, Giv58b, Giv58a, RTDL94, Giv52, Giv54, HS86, Meg93, RW61, Wu16, Xu88, BG64]. means [Dua88]. measurement [PW18]. memory [CDR89, PZN96]. merging [Liu86]. Mesh [MBM98]. Mesh-Connected [MBM98]. Method [HW79, Ips84, Joh61, Giv53, HS86, KK78, LLR^{+}90, RW61, Tan82, Tan83, YH09]. methods [BY09, PDW02, YH09]. Miller [Giv51]. MIMD [KKK83]. MIMO [FA17]. minimum [ZXLL17]. Model [Cla81, Ste97, GLN84, GLN86a, GLN86b, Kon00]. Modern [HH18]. modification [MM86, Mär87]. Modifications [Ham74]. Modified [BY09, HW79, Hop97, Joh61, HH04]. Modifikation [MM86]. Moving [Cla81]. Multiprocessors [BG88].

National [CRTQ86, Yoo05]. negative [BW84]. network [BKŻ16, BKŻ17, Dua88, HB97]. Neumann [VG55]. neural [BKŻ16, BKŻ17, HB97]. Neuts [Mar67]. Non [BW84, MAMB14]. Non-negative [BW84]. non-orthogonal [MAMB14]. Nonorthogonal [Sou09]. nonsymmetric [MCLM20]. Norm [HH18]. Note [Ham74, BMY13]. Numeric [HK87]. Numerical [Giv54].

Olkin [Mar67]. One [Cla81]. Operations [Ste97]. operators [LS17]. opposite [Abd18, Mar18]. opposite-bordered [Abd18, Mar18]. Optical [GV87]. Optimal [CD94]. optimization [KK78]. Optimizing [BG88]. orbit [dMdSK07]. order [MCLM20, SAMAN18]. Ordering [GO95, MC84, CM99, Duf74, GLN84, GLN86a, GLN86b, HLP81, Ost87]. Orthogonal [GL87, PR87, Rat82, BY09, MAMB14, OB94, PDW02, PR89, ZHF95a, ZHF95b]. orthogonalization [YH09]. Orthonormal [Bro98, DV00, DV03]. Overcoming [Ji88].

Parallel [BKŻ17, CUM86, CRTQ86, CD94, Dua88, HGP86, Ips84, Kon00, RTDL94, CDMR86, CDR89, ZHF95a, ZHF95b]. parameter [PW18]. parameterized [CM99]. parameters [Xie88]. Parametric [Giv47, FsH20]. parametrized [Del98]. PC [HK87]. PC-BLAS [HK87]. Performances [Del98]. Pipeline [HK06, CM99]. pipeline-efficient [CM99]. pipelined [HS86, PW18]. Pipelining [PZN96]. Pivot [Duf74]. Plane [Giv58a, Ham74]. PRAM [CD94, HK06, Kon00]. Preconditioned [YH09]. prior [HLP81]. Problem [Giv57, GLN86b, Tan82, Wu16]. Problems [BI87, BB38, BGW38a, BC38, BGW38b, CBK^{+}37, CB38, Cam38, GS91, HW79, HRH^{+}62, HM63, HYG63, HT63, KS38, Mar67, MS38, RP63, TB38, WW63, GH80, HLP81, Ost87, Tan83, YH09]. proceedings [CRTQ86]. Processes [Wil57, RW62]. processing [Dua88]. Processor [HK87]. Processors [MBM98]. Produced [Wil57]. Professors [VG55]. Programming [HW79]. Projective [Giv34]. Property [BG64]. proposed [Giv68]. pruning [HB97]. pseudo [Ji88]. pseudo-Givens [Ji88]. pseudospectra [LS17]. Publications [Giv51, Giv59].

QAM [SAMAN18]. QRD [SPC^{+}16]. quaternion [JO03, JO04, JO05]. quaternion-valued [JO04].

R [Giv51, Mar67]. Rank [DV08, Kon02]. rank- [Kon02]. RBF [HB97]. Real [RTDL94, Giv54]. realisation [PW18]. really [Han73]. reciprocal [Bor21]. reconstruction [RASSI10]. rectangular [CR88]. recursive [OB94]. recursively [Xie88]. Recycling [LS17]. reduction [Duf74, HLP81, JO04, Meg93, Ost87, ZQW14, ZHF95b]. reductions [JO05]. Reference [HH18]. Reflections [GL87]. register [CM99]. register- [CM99]. regression [BW84]. reliable [Abd18, Mar18]. reliably [BDKM00, BDKM02]. Remark [DG82, Dod83, HH18, HH04]. Rencontres [CRTQ86]. Reports [Giv62]. Representation [DV08, PJM^{+}21, OB94]. resolution [RASSI10]. response [PW18]. restrictions [FsH20]. Restructuring [Hop97]. results [Giv53, PDW02]. Review [BG64, Jon06]. Root [GS91, Bor21, Dua88]. Roots [Gen73]. Rotation [GV87, GS91, Ham74, SPC^{+}16, DS88, DS89, Döh88, Döh89, Döh91, FA17, HB97, PW18, SVTD19, Wu16, ZXLL17]. Rotation-Based [SPC^{+}16, FA17]. Rotationen [MM86]. Rotations [BI87, GL87, GO95, Giv58a, Ips84, MBM98, Rat82, BY09, BW84, BKŻ16, BKŻ17, BDKM00, BDKM02, Bor21, Dua88, FsH20, GHL^{+}19, GH80, LS17, MM86, Mär87, MAMB14, MCLM20, PC99, PDW02, SAMAN18, Sou09, VKS^{+}15, Yub91, dMdSK07]. Routine [Hop97]. Row [GLN84, GLN86a, GLN86b, Duf74, Liu86, Ost87]. Row-ordering [GLN84, GLN86a, GLN86b, Ost87].

Scaled [BI87]. Scattered [CUM86]. scheme [RW61]. schemes [GLN84, GLN86a, GLN86b, Liu86]. schnellen [MM86]. Science [Yoo05]. Section [Giv62]. Sections [Giv62]. selection [Duf74]. seminar [VG55]. separable [PW18]. separation [SAMAN18]. sequences [HK06, Kon00]. sequential [dMdSK07]. shared [CDR89]. Shear [MAMB14]. short [BMY13]. sign [FsH20]. signatures [Giv40]. Similarity [Rat82]. Simple [Wu16, dMdSK07]. simplex [Yub91]. skewed [Wu16]. Slow [GLJ^{+}91]. Smith [BG64]. smoothing [Bla85]. Societies [Giv62]. Software [HLP81]. Solution [BI87, CBK^{+}37, GH80, HRH^{+}62, Giv47, Tan82, Tan83]. Solutions [BB38, BGW38a, BC38, BGW38b, CBK^{+}37, CB38, Cam38, HRH^{+}62, HM63, HYG63, HT63, KS38, Mar67, MS38, RP63, TB38, WW63]. solver [PZN96, VKS^{+}15]. Solving [GS91, MBM98, Abd18, HGP86, Kon00, Mar18]. Some [Cau58]. source [SAMAN18, Wu16]. sources [Wu16]. Spaces [Giv36, Giv37b, Giv37a]. Sparse [GL87, GO95, RASSI10, ZXLL17, Duf74, GH80, GLN84, GLN86a, GLN86b, HS86, HLP81, Liu86, Ost87, Tan82, Tan83, YH09]. special [YJ01]. spinors [Giv34]. Square [Gen73, GS91, Bor21, Dua88]. Squared [Döh88, Döh91, Döh89, ZXLL17]. Squares [BI87, Gen73, GS91, Bla85, GH80, HLP81, OB94, Ost87, Tan82, Tan83, Xie88, YH09, dMdSK07]. standard [HH04]. Statistical [Döh89]. Statistics [Jon06]. Stiefel [PJM^{+}21]. store [RW61]. Stratagem [CUM86]. Structured [DV08]. structures [PW18]. Subprograms [DG82, HK87, LHKK79, LN88]. Subroutines [Dod83]. subspace [PC99]. suggested [Giv53]. SVARs [FsH20]. SVD [PC99]. SVD-based [PC99]. Symbolic [Ost87]. Symmetric [RTDL94, Ste97, Giv53, Giv54, RW61]. symplectic [YJ01]. system [RASSI10]. systems [Abd18, FA17, Mar18]. Systolic [BI87, CR88, GS91, CDMR86, DS88, DS89].

T [BG64]. tableau [Yub91]. Tankard [Giv59]. technique [SVTD19, Wu16]. Tensor [Giv36, Giv37b, Giv37a]. tensors [MCLM20]. terminology [FC06]. Theoretic [Ste97]. Theory [Giv59]. Thrall [Giv51]. Tolerant [MBM98]. tool [Ace11]. tracking [PC99]. Transformation [Bro98, Hop97, RTDL94, SPC^{+}16, Yub91, BMY13, Han73, JO03, JO05, LCZ97, Xie88, Xu88, ZXLL17]. Transformations [Gen73, Gen75, HW79, Rat82, Bla85, DV00, DV03, GLN84, GLN86a, GLN86b, HH04, HGP86, Ji88, KK78, KKK83, Liu86, YJ01]. Transforming [Giv58a]. Translation [HK87, LN88]. transputer [Dua88]. Triangular [Giv58a]. triangularisation [Meg93]. Triangularization [GV87, ZHF95a]. tridiagonal [Abd18, LLR^{+}90, Mar18, VKS^{+}15]. Tridiagonalization [CUM86]. Tridiagonalizing [RTDL94]. two [RW61, Wu16]. two-level [RW61]. two-source [Wu16].

Unitary [BG64, Giv58a, MCLM20].

Updating [HW79, Kon02]. upper [JO04]. Uppuluri [Mar67]. Usage [DG82, Dod83, HK87, LHKK79, LN88]. use [Ace11, PC99]. Using [CUM86, GV87, HW79, Ips84, RTDL94, BY09, Bla85, GHL^{+}19, GH80, HGP86, PDW02, SAMAN18, ZQW14, ZXLL17, dMdSK07]. utilising [FsH20].

V. [Mar67]. Value [Giv57]. Value-Vector [Giv57]. valued [JO03, JO04, JO05]. values [Giv52, Giv54]. Veblen [VG55]. Vector [Giv57]. vectors [JO03]. versus [GL87]. via [PJM^{+}21]. visit [HH04].

W [Mar67]. Wallace [Ano93, GP91, Mar67, Poo93, Poo94]. Weight [DV08]. Without [Cla81, Gen73]. Workshop [CRTQ86].

References

AbderramanMarrero:2018:RGA

[Abd18] J. Abderramán Marrero. A reliable Givens–LU approach for solving opposite-bordered tridiagonal linear systems. Computers and Mathematics with Applications, 76(10):2409–2420, November 15, 2018. CO-DEN CMAPDK. ISSN 0898-1221 (print), 1873-7668 (elec-

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Acerbi:2011:LGF

[Ace11] Fabio Acerbi. The language of the “Givens”: its forms and its use as a deductive tool in Greek mathematics. Archive for History of Exact Sciences, 65(2): 119–153, 2011. CODEN AHE-SAN. ISSN 0003-9519 (print), 1432-0657 (electronic).

Anonymous:1993:JWG

[Ano93] Anonymous. James Wallace Givens Jr. *36. Princeton Alumni Weekly Web site, 1993.

URL https://paw.princeton.
edu/memorial/james-wallace-
givens-jr-36.

Bennett:1938:PSE

[BB38] A. A. Bennett and J. H.

Butchart. Problems and solutions: Elementary problems: Solutions: E289. American Mathematical Monthly, 45(3):186–187, March 1938. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See also [CBK^{+}37].

Butchart:1938:PSEa

[BC38] J. H. Butchart and W. B. Clarke.

Problems and solutions: Elementary problems: Solutions: E293. American Mathematical Monthly, 45(3):189, March 1938. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See also [BGW38b, CBK^{+}37].

Bindel:2000:CGR

[BDKM00] D. Bindel, J. Demmel, W. Kahan, and O. Marques. On computing Givens rotations reliably and efficiently. LAPACK Working Note 148, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 2000.

URL http://www.netlib.org/
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Bindel:2002:CGR

[BDKM02] David Bindel, James Demmel, William Kahan, and Osni Marques. On computing Givens rotations reliably and efficiently. ACM Transactions on Mathematical Software, 28(2):206–238, June 2002. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic). See original LAPACK Working note in [BDKM00].

Burrows:1964:BRP

[BG64] James W. Burrows and Wallace Givens. Book review: On a Property of a Unitary Matrix (J. L. Brenner and F. T. Smith). SIAM Review, 6(4): 460–461, ???? 1964. CO-DEN SIREAD. ISSN 0036-1445 (print), 1095-7200 (electronic).

Bernstein:1988:OGA

[BG88] Herbert J. Bernstein and Max Goldstein. Optimizing Givens’ algorithm for multiprocessors. SIAM Journal on Scientific and Statistical Computing, 9(3):601– 602, May 1988. CODEN SI-JCD4. ISSN 0196-5204.

Butchart:1938:PSE

[BGW38a] J. H. Butchart, Wallace Givens, and R. J. Walker. Problems and solutions: Elementary problems: Solutions: E293. American Mathematical Monthly, 45(8): 552–553, October 1938. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See also [BC38, CBK^{+}37].

Butchart:1938:PSEb

[BGW38b] J. H. Butchart, Wallace Givens, and R. J. Walker. Problems and solutions: Elementary problems: Solutions: E293. American Mathematical Monthly, 45(8): 552–553, October 1938. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See also [BC38, CBK^{+}37].

Barlow:1987:SGR

[BI87] Jesse L. Barlow and Ilse C. F.

Ipsen. Scaled Givens rotations for the solution of linear least squares problems on systolic arrays. SIAM Journal on Scientific and Statistical Computing, 8(5): 716–733, September 1987. CO-DEN SIJCD4. ISSN 0196-5204.

Bilski:2016:AGR

[BKŻ16] Jarosław Bilski, Bartosz Kowalczyk, and Jacek M. Żurada. Application of the Givens rotations in the neural network learning algorithm. In Artificial intelligence and soft computing. 15th international conference, ICAISC 2016, Zakopane, Poland, June 12–16, 2016. Proceedings. Part I, pages 46–56. Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 2016. ISBN 3-319-39377-4; 3-319-39378-2.

Bilski:2017:PIG

[BKŻ17] Jarosław Bilski, Bartosz Kowalczyk, and Jacek M. Żurada. Parallel implementation of the Givens rotations in the neural network learning algorithm. In Artificial intelligence and soft computing. 16th international conference, ICAISC 2017, Zakopane, Poland, June 11–15, 2017. Proceedings. Part I, pages 14–24. Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 2017. ISBN 3-319-59062-6; 3-319-59063-4.

Blais:1985:LSF

[Bla85] J. A. R. Blais. Least-squares filtering and smoothing using Givens transformations. Manuscripta Geodaetica, 10:208– 212, 1985. ISSN 0340-8825.

Biloti:2013:SNG

[BMY13] R. Biloti, L. C. Matioli, and Jinyun Yuan. A short note on a generalization of the Givens transformation. Computers and Mathematics with Applications, 66(1):56–61, August 2013. CO-DEN CMAPDK. ISSN 0898-1221 (print), 1873-7668 (elec-

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Borges:2021:FCA

[Bor21] Carlos F. Borges. Fast compensated algorithms for the reciprocal square root, the reciprocal hypotenuse, and Givens rotations. arXiv.org, ??(??):1–11, February 23, 2021. URL https:

//arxiv.org/abs/2103.08694.

Brookner:1998:GOT

[Bro98] Eli Brookner. Givens Orthonormal Transformation, pages 283– 314. Wiley, New York, NY, USA, April 1998. ISBN 0-471-18407-1 (print), 0-471-22419-7 (e-book).

Bates:1984:NNR

[BW84] Douglas M. Bates and Dennis A.

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Causey:1958:SEB

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[CRTQ86] Michel Cosnard, Yves Robert, Maurice Tchuente, and Patrice Quinton, editors. Parallel algorithms & architectures: proceedings of the International Workshop on Parallel Algorithms & Architectures, Centre National de Rencontres Mathématiques, Luminy, France, 14–18 April, 1986. North-Holland Publishing Co., Amsterdam, The Netherlands, 1986. ISBN 0-444-70104-4. LCCN QA76.5 .I618 1986.

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[Giv34] J. W. Givens, Jr. Projective differentiation of spinors. Proceedings of the National Academy of Sciences of the United States of America, 20:232–233, 1934. CO-DEN PNASA6. ISSN 0027-8424 (print), 1091-6490 (electronic).

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[Giv40] Wallace Givens. Factorization and signatures of Lorentz matrices. Bulletin of the American Mathematical Society, 46:81– 85, 1940. CODEN BAMOAD. ISSN 0002-9904 (print), 1936-881x (electronic).

Givens:1947:PSL

[Giv47] Wallace Givens. Parametric solution of linear homogeneous Diophantine equations. Bulletin of the American Mathematical Society, 53:780–783, 1947. CO-DEN BAMOAD. ISSN 0002-9904 (print), 1936-881x (electronic).

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Givens:1952:FVM

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[Giv53] Wallace Givens. A method of computing eigenvalues and eigenvectors suggested by classical results on symmetric matrices. In Simultaneous linear equations and the determination of eigenvalues, volume 29 of National Bureau of Standards Applied Mathematics Series, pages 117–122. United States Government Printing Office, Washington, DC, USA, 1953.

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Givens:1957:CVV

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Givens:1959:RPI

[Giv59] Wallace Givens. Recent publications: Introduction to the Theory of Determinants and Matrices, by Edward Tankard Browne. American Mathematical Monthly, 66(3):247–248, March 1959. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Givens:1962:RSS

[Giv62] Wallace Givens. Reports of sections and societies: Mathematics (section a). Science, 135(3503): 547–549, February 16, 1962. CO-DEN SCIEAS. ISSN 0036-8075 (print), 1095-9203 (elec-

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Ordering Givens rotations for sparse QR factorization. SIAM Journal on Matrix Analysis and Applications, 16(3):1024–1041, July 1995. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic). URL http://

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Gotze:1991:SRD

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A square root and division free Givens rotation for solving least squares problems on systolic arrays. SIAM Journal on Scientific and Statistical Computing, 12(4): 800–807, July 1991. CODEN SI-JCD4. ISSN 0196-5204.

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A pipelined Givens method for computing the QR factorization of a sparse matrix. Linear Algebra and its Applications, 77 (??):189–203, May 1986. CO-DEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (elec-

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