A Bibliography of Publications by, and about, Magnus Rudolph Hestenes

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/

05 June 2024 Version 1.05

Abstract

This bibliography records publications of Magnus Rudolph Hestenes.

Title word cross-reference

Ax = λBx [HK51a]. E [Hes46c].

-function [Hes46c].

13-15 [Cra87]. 1968 [ZNB69]. 1970 [Rei71a]. 1987 [Cra87].

2 [Tab70]. 23 [PT53]. 2nd [ZNB69].

447 [Jer77].

6 [Tab70].

70th [Rus76].

Academic [Tab70]. Accelerated [Jit80]. ACM [Cra87]. adaptive [DLLL19]. adjoint [Hes61c]. affine [DHG^{+}17]. Algebra [Hes62c, LH91, Hes73b, SM02]. algebraic [FHW48, Mae54]. algebraischer [Mae54]. algebras [BI64]. Algorithm [SLLT18, WZ14, LLW22, YZ13, YML16]. Algorithms [Ano22, DS00, GO89, HWY20, WSH^{+}17, Wan23]. alternate [Hes47a]. analogue [Hes41b]. Analysis [HT91, PT53, Hes54, Hes76b, Hes87]. Andenken [Zus79]. Anelli [BP77]. Angeles [PT53]. application [HM40, HWY20, LLW22]. Applications [Hes50b, Hes51a, Hes62c, LH91, Rei71a]. applied [Roc73]. appreciation [Mie74]. approach [BKG15, SM02]. April [Rei71a]. Armijo [DW12]. articles [Ano74]. Artinian [Cag80, Pro77]. artiniani [BP77]. Auflösung [Mae54]. Augmentability [Hes80a]. augmented [wDLLQ09, For75]. August [PT53].

B70 [Tab70]. B70-6 [Tab70]. Balakrishnan [Dre65, Tab70]. based [BKG15, Sug14, WSH^{+}17, Zha09]. basis [Hes34a]. Beckenbach [Dea64]. BFGS [BKG18]. bilateri [BP77]. Biorthogonalization [Hes58]. Bipedal [SLLT18]. birthday [Rus76]. Bolza [BH33a, Hes33c, Hes34a, Hes34c, Hes34d, Hes34e, Hes36c, Hes36b, Hes37, Hes39, Hes42, Hes46a, Hes47a, Hes47b]. Book [Buk67, Cul77, Dea64, Dre65, Jer77, Ste82]. boundary [Sny82]. Bounded [Gui65a].

calculation [HK51b]. Calculus [BH35a, BH35c, BH35d, Buk67, Hes33e, HB33, Hes34d, Hes49, Hes50a, Hes50b, Hes56b, Hes66b, Hes80b, Hes13, Rus76, You68, BH35b, BH32, BH33a, BH33b, Bol01, Hes33a, Hes33d, Hes33c, Hes34b, Hes34c, Hes34e, Hes36c, Hes37, Hes38, Hes39, HR39, HM40, Hes41b, Hes42, Hes46a, Hes46b, Hes46c, Hes48, Hes51a, Hes66a]. California [PT53]. Case [Hes75b, Cul77, Jer77]. Catherine [Rei71a]. Center [Rus76]. Century [Ano22, Lid01]. certain [HR74a, HR74b]. CG [CLS24, HAE21]. characteristic [HK51b]. characterization [Sci77]. Chisholm [Rus76]. Chronicle [Lid01]. class [Wan23]. close [RLHK51]. coefficient [RMMF10]. Collection [Ano74]. College [Rei71a]. combination [DHG^{+}17, Rup75]. combined [BGR05]. Computation [Cra87]. computational [Hes55]. Computer [Lee95, Zus79]. Computerentwicklung [Zus79].

Computing [Nas90, ZNB69, ZNB69, Dre65, Tab70]. condition [DLHY15, Hes33a, Hes34b, HR39, Pel91, Zha09]. Conditions [BH35c, BH35d, Hes32b, HB33, Hes34d, BH32, BH33b, Hes31, Hes32a, Hes33b, Hes33d, Hes33c, Hes34e, Hes36b, Hes46a, Hes48, KBA23b]. conducted [Rus76]. Conference [Cra87, Rei71a, ZNB69]. Conjugacy [Hes87, Hes90, DLHY15, KBA23b]. Conjugate [GO89, HS52, Hes56a, Hes75c, Hes78a, Hes80c, O’L01b, Rai17, Rei71b, SLLT18, AFP19, BKG15, BKG17, BSA18, DC05, DW12, DLHY15, DLL^{+}17, DHG^{+}17, DLLL19, FA21, GXS95, Heg88b, Heg88a, HWY20, KBA23b, LLW22, NK21, QHL96, RMMF10, SW15, SA16, Shi01, WSH^{+}17, Wan23, WHT10, YZ13, YML16, Zha09, Ste82]. Considered [Gui65b]. considering [KBA23a]. constrained [wDLLQ09, HKH^{+}22, SL15]. constraints [AKAW19]. Contributions [Hes33e]. Control [Buk67, Hes65, Hes66b, Hes69c, Hes80b, Rus76, You68, Dur99, Hes64, Hes66a, Hes75a, Hes76a]. Controller [SLLT18]. Convergence [Rai17, BSA18, DW12, GXS95, Jit80, SW15, Sci77, Shi01, SL15, WHT10, ZZ12, ZZ13]. Convergent [SLLT18]. convex [AKAW19, Roc73]. Coordinates [Gui65a]. critical [Hes45]. CUDA [CMN18].

Dai [BKG15, NK21]. Dan [DC05]. Date [Ano22]. Deaths [Ano91a]. Decomposition [WZ14]. decompositions [BI64]. Dedicated [Rus76, Ano74]. derivative [HKH^{+}22]. derivative-free [HKH^{+}22]. Derivatives [Rai17]. descent [BKG17, BSA18, DLHY15, KBA23a, KBA23b, SRMM14, Wan23]. Describing [CC97]. Determination [Hes53, PT53]. development [Zus79]. differentiable [For75, Hes41a]. Differential [O’L01a, Hes61b, HG68]. Dimensional [Cul77, Hes75b, Jer77]. direct [BI64, Heg88b, Hes37]. Direction [Hes80c, Rai17, Ste82, Hes78a]. directions [Heg88b, Heg88a]. Discovers [Ano22]. discrete [Dur99]. dual [SW75].

Edited [Dea64]. Editors [DS00]. Eds [Tab70]. Eduard [Zus79, Zus79]. Edwin [Dea64]. effective [Cag80]. effettivi [BP77]. efficient [DLLL19, SA16]. Eigenvalue [O’L01a]. Eigenvalues [PT53, Hes53, RLHK51]. eigenvectors [Hes53]. Elementary [Hes50a]. Elements [Hes56b, Hes66a, Hes13]. elliptic [Hes61b]. embedding [HG68]. End [Hes32b, Hes31, Hes33b]. End-Points [Hes32b, Hes31]. Endpoint [Hes49]. endpoints [Hes32a]. Engineer [Bec56, Bec62, Bec13a, Bec13b, Dea64]. Engineering [LH91, SW75]. Equation [Rei71b]. Equations [AMI^{+}21, Hes51b, HS51, PT53, Rei71a, AKAW19, AWK^{+}20, FHR51, FHW48, HKH^{+}22, Hes61b, HG68, Hes73a, HS73, Mae54, SL15, YML16]. ETH [Zus79, Zus79]. Exactness [wDLLQ09]. examples [CLS24]. Excellence [Lid01]. Extension [Hes41a, DLLL19, FW98a, FW98b, Pel91]. Extensions [BKG17].

F [Dea64, You68]. family [KBA23a, KBA23b]. Finite [Cul77, Hes75b, Jer77]. First [Bec56, Bec13a]. Fixed [Hes49]. form [Hes34c, Hes36c, Hes47b]. Formalization [CC97]. Forms [Hes68, HM40, Hes51a]. FPGA [WZ14]. free [HKH^{+}22]. function [wDLLQ09, Hes41a, Hes46c]. functionals [For75, HR74a, HR74b]. Functions [Hes36a, FW98a, FW98b].

Gage [Fri73]. gaps [SW75]. General [Heg88b, Heg88a, Hes32b, Hes50b, Hes31, Hes33b]. Generalized [BH35a, BH35b, FW98a, FW98b, Hes39, FW08]. German [Mae54, Zus79]. Gleichungen [Mae54]. Global [DW12, GXS95, BSA18, SW15, Shi01]. GMRES [CLS24]. GPU [CMN18]. GPU-CUDA [CMN18]. Gradient [GO89, Hes56a, SLLT18, AFP19, BKG15, BKG17, BSA18, DC05, DW12, DLHY15, DLL^{+}17, DHG^{+}17, DLLL19, FA21, GXS95, Hes69a, Hes69b, HWY20, KBA23b, LLW22, NK21, QHL96, RMMF10, SW15, SA16, Shi01, WSH^{+}17, Wan23, WHT10, YZ13, YML16, Zha09]. Gradients [HS52, Hes75c, O’L01b, Rei71b, HK51b, Hes87, Hes90]. Gram [Rai17]. Green [Hes41b]. Guest [DS00].

held [PT53, Rei71a]. Hermitian [Hes61a]. Hestene [Rai17]. Hestenes [Buk67, Cul77, Jer77, AMI^{+}21, AFP19, Ano74, Ano91a, Ano91b, Anoxx, AKAW19, AWK^{+}20, BKG15, BKG17, BKG18, BF81, BSA18, BP77, BI64, BCH^{+}91, Ber92, BGR04, BGR05, Cag80, Cag81, Cha91, CC97, CMN18, DC05, DW12, DLHY15, DLL^{+}17, DHG^{+}17, DLLL19, wDLLQ09, Dur99, FA21, FW98a, FW98b, FW08, For75, Fri73, Gui65a, Gui65b, GXS95, HAE21, Han88, HKH^{+}22, Heg88b, Heg88a, HWY20, JBM21, Jit80, KBA23a, KBA23b, Lee95, LLW22, Mie74, NK21, Pel91, Pro77, QHL96, RMMF10, Roc73, Rup75, SW15, SA16, Sci77, SRMM14, Shi01, Smi69, Sny82, Spe76, Spe78, Ste82, SW75, Ste68, Ste73, Sug14, SM02, SL15, SLLT18, WZ14, WSH^{+}17, Wan23, WHT10, You68, YZ13, YML16, Zha09, ZZ12, ZZ13]. Hilbert [Hes51a, Hes54, Hes61c]. Hill [Dea64]. History [Cra87, GO89, Nas90]. HSNC’87 [Cra87]. hybridization [BKG15, BKG18, NK21]. Hypotheses [Gui65b].

ideal [Cag81]. ideali [BP77]. ideals [Cag80]. II [Heg88a, Hes34e, HR74b]. Image [AMI^{+}21, CC97, HKH^{+}22, HWY20, Wan23]. Implementation [CMN18, WZ14]. INA [HT91]. indefinite [BGR04]. indirect [Hes47b]. inequality [wDLLQ09]. inexact [BGR05]. Institute [HT91, PT53, Rei71a]. Integral [O’L01a, Hes48]. interior [BGR04]. interior-point [BGR04]. International [ZNB69]. Introduction [DS00, Hes50a, Hes62a, Hes62b, Smi69]. inverse [Sug14]. Inversion [Hes58]. Isoperimetric [BH35c, BH35d, Hes38, Hes46a]. Italy [ZNB69]. Iteration [O’L01a]. Iterative [FHR51, Hes51b, Hes55, Hes73a, Mae54]. iterativen [Mae54].

Jacobi [CMN18, Hes33a, Hes34b, WZ14]. Jacobi-One-Sides [CMN18]. Jacobson [Ste68, Ste73]. Jersey [Cra87]. John [Jer77].

Karush [BGR05]. kinematics [Sug14]. Kuhn [BGR05].

L [Tab70]. Lagrange [Hes33d, Hes34a, Hes36b]. Lagrangian [wDLLQ09, For75]. Lanczos [GO89]. Large [Rei71a, Rei71b, DLL^{+}17, Wan23, YZ13, YML16]. large-scale [DLL^{+}17, Wan23, YZ13, YML16]. Laurence [Rus76]. Least [Hes50b, BKG15]. least-squares [BKG15]. lemma [FW98a, FW98b, FW08]. light [SM02]. like [AKAW19]. Lindeberg [Hes46b]. line [DW12, JBM21]. Linear [CC97, Hes51b, HS51, HS52, Hes56a, Hes62c, LH91, O’L01a, O’L01b, PT53, Rei71a, Rei71b, BKG18, FHR51, FHW48, Hes61b, Hes73a, HS73, NK21, SL15]. London [Jer77]. Lucien [Dre65].

M [Mie74]. M. [Buk67]. Madison [Rus76]. Magnus [Cul77, Jer77, Ste82, Ano74, Ano91a, Ano91b, Anoxx, BCH^{+}91, Ber92, Cha91, Lee95, You68]. Mathematics [Bec56, Bec62, Bec13a, Bec13b, Dea64, LH91, Rei71a, Rus76]. Matrices [Hes58, Hes62c, Hes53, Hes61a]. matrix [HK51b, RLHK51]. May [Cra87]. Mayer [BH32, BH33b, Hes31, Hes32b, Hes32a, Hes33b, HB33]. McGraw [Dea64]. McGraw-Hill [Dea64]. Measurements [Lid01]. memory [Ber92, Zus79]. memoryless [BKG18]. Method [AMI^{+}21, CMN18, HAE21, Han88, Hes56a, O’L01a, Rai17, Rei71b, AFP19, AKAW19, AWK^{+}20, BKG18, BSA18, BGR04, BGR05, DC05, DW12, DLHY15, DLLL19, Dur99, FA21, For75, GXS95, HKH^{+}22, HK51b, Jit80, KBA23a, KBA23b, NK21, QHL96, Roc73, Rup75, SW15, SA16, Sci77, SRMM14, Shi01, Sny82, SW75, Sug14, SL15, WHT10, Zha09, ZZ12, ZZ13]. Methods [Hes49, Hes51b, HS52, Hes80c, O’L01b, Ste82, Tab70, ZNB69, BKG15, BKG17, DLL^{+}17, DHG^{+}17, Dre65, FHR51, Hes54, Hes55, Hes69a, Hes69b, Hes73a, Hes78a]. minimal [Cag81]. Minimax [BH35a, Hes36a, BH35b]. Minimization [For75, HS51, HS73, HR74a, HR74b]. minimizations [YML16]. mixed [DC05]. Modern [Bec56, Bec62, Bec13a, Bec13b, Dea64]. modification [JBM21, SA16, SRMM14]. Modifications [HAE21]. Modified [RMMF10, AFP19, BSA18, DW12, DLHY15, DLL^{+}17, HWY20, KBA23b, LLW22, QHL96, Shi01, SL15, WHT10, YZ13, YML16, ZZ13]. Monotone [AMI^{+}21, AKAW19, AWK^{+}20]. Motroni [Fri73]. multiple [Hes48]. Multiplier [Hes69a, Hes69b, BGR05, Jit80, Roc73, Rup75, Sug14]. multipliers [Sci77, SW75].

Natural [BH35c, BH35d]. NBS [Ano22, HT91, Lid01]. NBS-INA [HT91]. NBS/NIST [Lid01]. necessary [Pel91]. Neustadt [Tab70, Dre65]. Newton [BGR05, KBA23a, Rup75]. NIST [Lid01]. no [Cag80]. non [For75]. non-differentiable [For75]. nonconvex [ZZ13]. Nonlinear [AMI^{+}21, AKAW19, AWK^{+}20, DW12, HKH^{+}22, SA16, Sny82, SL15, YML16, Zha09]. nonmonotone [DLL^{+}17]. nonparametric [Hes47b]. nonsmooth [YML16]. normal [Hes47a]. note [BH33a, Hes33a, Hes34b, HR39, ZZ12]. Notes [FHW48]. Number [Han88]. Numeric [Cra87]. Numerical [Dur99, Hes49, HT91, PT53, Rai17, Hes54]. NY [Tab70].

Obituary [BCH^{+}91]. Obtaining [Hes49]. occasion [Rus76]. One [Ano22, CMN18]. Operator [AMI^{+}21]. Operators [O’L01a, Hes61c]. Optimal [Buk67, Hes65, Hes66b, Hes69c, Hes80b, SLLT18, You68, AFP19, Dur99, Hes64]. Optimization [HAE21, Hes75b, Hes80c, Rai17, Tab70, ZNB69, Dre65, wDLLQ09, Hes78a, Hes78b, Hes80a, NK21, RMMF10, SW75, Wan23, YZ13, Zha09, ZZ13, Ste82, Cul77, Jer77]. optimum [Hes66a]. original [ZZ12]. Osgood [Bol01]. Oxford [Rei71a, Rei71a].

Pairs [Hes68]. Papers [ZNB69, Cra87]. Parallel [CMN18]. parameter [AWK^{+}20]. parametric [Hes33a, Hes34b, Hes34c, Hes36c]. partial [Hes61b]. Path [Hes28]. Paths [Hes50b]. Pioneers [Lee95]. point [BGR04, Sny82]. Points [Hes32b, Hes31, Hes33b, Hes45]. Polak [BKG17]. polarization [SM02]. Polyak [BKG17]. Powell [wDLLQ09, For75, Jit80, Roc73, Rup75, Sug14]. pp [Tab70]. pp. [Dea64]. presented [Cra87, ZNB69]. Press [Tab70]. Primitive [Cag81]. Princeton [Cra87]. Principle [BH35a, Hes36a, BH35b]. prioritized [Sug14]. privi [BP77]. Problem [Gui65a, Gui65b, Hes32b, HB33, Hes34d, Hes50b, O’L01a, BH32, BH33a, BH33b, Hes31, Hes32a, Hes33b, Hes33d, Hes33c, Hes34c, Hes34e, Hes36c, Hes37, Hes39, Hes42, Hes46a, Hes47a, Hes47b]. Problems [HAE21, Hes49, Tab70, ZNB69, DLL^{+}17, wDLLQ09, Dur99, Hes33a, Hes34a, Hes34b, Hes36b, Hes38, Hes48, Hes75a, Hes76a, Hes78b, Hes83, Sny82, Wan23, Dre65]. Proceedings [Rei71a, Cra87, PT53, Rus76]. processing [AWK^{+}20]. Professor [Mie74]. programming [Roc73]. Projected [SLLT18]. projection [AKAW19, AWK^{+}20, LLW22, SL15]. proof [Bol01, Hes37, Hes38, Hes47a, Hes47b]. properties [wDLLQ09, SRMM14, ZZ12]. property [AFP19, BKG17, BSA18, SA16]. pseudoinverse [Hes76b]. Pseudoinverses [Hes75c]. Publications [Lid01].

Quadratic

[Hes61b, Hes68, Hes75a, Dur99, HM40, Hes51a, HR74a, HR74b, Hes76a, Hes83]. quasi [KBA23a]. quasi-Newton [KBA23a]. Quasiprimitive [BF81].

R [Ano74, Ano91a, Ber92, Buk67, Cul77, Jer77, Lee95, Mie74]. Radical [Spe76]. range [Hes41a]. Rapidly [SLLT18]. rate [SL15]. Rates [Rai17]. real [HK51b, RLHK51]. recursion [Heg88b, Heg88a]. recursions [Heg88b, Heg88a]. Reducing [Han88]. Related [Hes58]. Relative [Hes61a, Hes61c]. Remarks [FW08]. Remo [ZNB69]. Replies [Fri73]. Report [Buk67]. Research [Rus76]. resolve [SW75]. restart [SA16]. Restoration [AMI^{+}21, HKH^{+}22, HWY20, Wan23]. Results [Hes58]. reverse [Heg88a]. Review [Cul77, Dea64, Dre65, Jer77, Ste82]. Reviews [You68]. Ribière [BKG17]. right [Cag80, Cag81]. ring [Spe76]. Rings [Ste68, BF81, Cag80, Cag81, Pro77, Smi69, Spe78, Ste73]. Robots [SLLT18]. Robust [Sug14, SLLT18]. role [Hes76b, Zus79].

Rolle [Zus79]. roots [HK51b]. Rotating [Hes28]. Rudolf [BCH^{+}91]. Rudolph [Anoxx].

San [ZNB69]. scale [DLL^{+}17, Wan23, YZ13, YML16]. scheme [BGR05]. Schmidt [Rai17]. Science [LH91]. Scientific [Cra87, Nas90]. search [DW12, JBM21]. secant [Zha09]. Second [Bec62, Bec13b]. Selected [Lid01]. self [Hes61c]. self-adjoint [Hes61c]. semplici [BP77]. Separation [RLHK51]. September [Rus76, ZNB69]. Series [Bec56, Bec62, Bec13a, Bec13b]. Sets [Rei71a]. sided [Cag80]. Sides [CMN18]. signal [AWK^{+}20]. Simple [Cag80, Pro77]. Simultaneous [PT53, FHW48]. Singular [Hes83, WZ14]. Solution [HS51, O’L01a, Rei71b, BGR05, Dur99, FHW48, HS73, Mae54, Sug14]. Solutions [Hes49, HK51a]. Solving [HAE21, Hes51b, HS52, Hes56a, Hes78b, O’L01b, FHR51, Hes73a, Sny82]. Some [DHG^{+}17, GO89, HWY20, For75]. Sons [Jer77]. Space [Gui65a, Hes51a, Hes54, Hes61c]. spacetime [SM02]. Sparse [Rei71a, Rei71b]. Spectral [SW15, AWK^{+}20, FA21, KBA23a, WSH^{+}17, Wan23]. Sphere [Hes28]. squares [BKG15]. St [Rei71a]. Standards [Lid01]. Steifel [RMMF10, SW15]. Stiefel [AMI^{+}21, AFP19, AKAW19, AWK^{+}20, BKG15, BKG17, BKG18, BSA18, DC05, DW12, DLHY15, DLL^{+}17, DHG^{+}17, DLLL19, FA21, GXS95, HAE21, HKH^{+}22, Heg88b, Heg88a, HWY20, JBM21, KBA23a, KBA23b, LLW22, NK21, QHL96, SA16, SRMM14, Shi01, Sny82, SL15, SLLT18, WSH^{+}17, Wan23, WHT10, YZ13, YML16, Zha09, ZZ12, ZZ13, Zus79]. Stiefel-like [AKAW19]. strong [JBM21, ZZ13]. Structure [Ste68, Ste73]. sufficiency [Hes37, Hes38, Hes47a, Hes47b]. Sufficient [BH32, BH33b, Hes31, Hes32b, Hes32a, Hes33b, HB33, Hes33d, Hes33c, Hes34d, Hes34e, Hes46a, Hes48, BKG17, BSA18, DLHY15, Hes36b, KBA23b]. sum [BI64]. Sweeps [Han88]. Sydney [Jer77]. symmetric [BGR04, HK51b, RLHK51]. Symposium [Rus76, PT53]. system [SW75]. Systems [HS52, Hes56a, O’L01b, Rei71b, BGR04, BGR05].

technique [BKG18]. Technology [Lid01]. Term [AMI^{+}21, BSA18, DHG^{+}17, DLLL19, FA21, HKH^{+}22, KBA23b, Wan23, ZZ12]. terms [LLW22]. ternari [BP77]. Ternary [Hes62c, Ste68, BF81, Cag80, Cag81, Hes73b, Pro77, Smi69, Spe78, Ste73]. Theorem [Hes46b, Bol01, Hes34a, HM40, Hes41b, HG68]. Theory [Cul77, Hes65, Hes66b, Hes69c, Hes75b, Hes80b, Rus76, Ste68, Hes45, Hes51a, Hes54, Hes61b, Hes64, Hes66a, Hes80a, Hes87, Jer77, Ste73, Buk67, You68]. Three [AMI^{+}21, BSA18, DHG^{+}17, DLLL19, FA21, HKH^{+}22, KBA23b, LLW22, Wan23, ZZ12]. Three-Term [AMI^{+}21, BSA18, DHG^{+}17, DLLL19, FA21, HKH^{+}22, KBA23b, Wan23, ZZ12]. Time [Hes50b]. Top [Ano22, DS00]. Toronto [Jer77]. Transformations [Hes62c]. Transforms [CC97]. Tribus [Fri73]. Tucker [BGR05]. Two [WSH^{+}17, Cag80, Sny82]. two-point [Sny82]. two-sided [Cag80]. Type [AMI^{+}21, DLL^{+}17, HKH^{+}22, Heg88b, Heg88a, Sny82].

UCLA [HT91]. Unconstrained

[HAE21, DLL^{+}17, NK21, RMMF10, Wan23]. understanding [CLS24]. University [Rus76]. use [SW75]. Using [CMN18].

V [Dre65, Tab70]. Value [WZ14, Sny82]. Variable [Hes32b, Hes31, Hes32a, Hes33b]. Variational [Gui65b, Hes64, Hes65, Hes69c, Hes54, Hes61b, Hes83, Hes87]. Variations [BH35a, BH35c, BH35d, Buk67, Hes33e, HB33, Hes34d, Hes49, Hes50a, Hes50b, Hes56b, Hes66b, Hes80b, Hes13, Rus76, You68, BH35b, BH32, BH33a, BH33b, Bol01, Hes33a, Hes33d, Hes33c, Hes34b, Hes34c, Hes34e, Hes36c, Hes37, Hes38, Hes39, HR39, HM40, Hes41b, Hes42, Hes46a, Hes46b, Hes46c, Hes48, Hes51a, Hes66a]. vectors [HK51b]. versions [Zha09].

W [Dre65, Tab70]. Walking [SLLT18]. Weakened [Gui65b]. Weierstrass [HR39, Hes46c]. Wiley [Jer77]. Wisconsin [Rus76]. without [Rai17]. Wolfe [JBM21].

xiii [Jer77]. xxii [Dea64].

York [Dea64, Jer77]. Young [Rus76]. Yuan [BKG15, DC05, NK21].

Zadeh [Tab70]. Zur [Mae54].

References

Amini:2019:MHS

[AFP19] Keyvan Amini, Parvaneh Faramarzi, and Nasrin Pirfalah. A modified Hestenes–Stiefel conjugate gradient method with an optimal property. Optimization Methods and Software, 34(4): 770–782, April 2019. ISSN 1026-7670 (print), 1055-6788 (electronic).

Awwal:2019:PHS

[AKAW19] Aliyu Muhammed Awwal, Poom Kumam, Auwal Bala Abubakar, and Adamu Wakili. A projection Hestenes–Stiefel-like method for monotone nonlinear equations with convex constraints. Thai Journal of Mathematics, 17:181– 200, 2019. ISSN 1686-0209.

Abubakar:2021:NTT

[AMI^{+}21] Auwal Bala Abubakar, Kanikar Muangchoo, Abdulkarim Hassan Ibrahim, Abubakar Bakoji Muhammad, Lateef Olakunle Jolaoso, and Kazeem Olalekan Aremu. A new three-term Hestenes–Stiefel type method for nonlinear monotone operator equations and image restoration. IEEE Access, 9:18262– 18277, 2021. ISSN 2169-3536.

Anonymous:1974:CAD

[Ano74] Anonymous. Collection of articles dedicated to Magnus R. Hestenes. Journal of Optimization Theory and Applications, 14(5):445–584, November 1974. CODEN JOTABN. ISSN 0022-3239 (print), 1573-2878 (elec-

tronic). URL https://link.
springer.com/journal/10957/
volumes-and-issues/14-5. 14

(1974), no. 5.

Anonymous:1991:DMR

[Ano91a] Anonymous. Deaths: Magnus R. Hestenes. Notices of the American Mathematical Society, 38(6): 657, July/August 1991. CO-DEN AMNOAN. ISSN 0002-9920 (print), 1088-9477 (electronic).

URL https://www.ams.org/
journals/notices/199107.

Anonymous:1991:MH

[Ano91b] Anonymous. Magnus Hestenes: 1906–1991. Notices of the American Mathematical Society, 38 (7):792, September 1991. CO-DEN AMNOAN. ISSN 0002-9920 (print), 1088-9477 (electronic).

URL https://www.ams.org/
journals/notices/199109.

Anonymous:19xx:MRH

[Anoxx] Anonymous. Magnus Rudolph Hestenes. Memorial Web site.,

19xx.  URL https://www.
findagrave.com/memorial/186188943/
magnus-rudolph-hestenes.

Anonymous:2022:NDO

[Ano22]  Anonymous.  NBS discovers

one of the century’s top 10 algorithms: Date 1952. NIST Web site, March 14, 2022.

URL https://www.nist.gov/
mathematics-statistics/nbs-
discovers-one-centurys-top-
10-algorithms. See [DS00].

Awwal:2020:PHS

[AWK^{+}20] Aliyu Muhammed Awwal, Lin Wang, Poom Kumam, Hassan Mohammad, and Wiboonsak Watthayu. A projection Hestenes–Stiefel method with spectral parameter for nonlinear monotone equations and signal processing. Mathematical & Computational Applications, 25 (2):Paper No. 27, 29, May 2020. ISSN 1300-686X.

Berkovitz:1991:OMR

[BCH^{+}91] Len Berkovitz, Tony Chan, Alfred Hayes, Dianne O’Leary, and Richard Tapia. Obituary. [Magnus Rudolf Hestenes]. SIAM News, 24(5):??, September 1991. ISSN 0036-1437.

Beckenbach:1956:MME

[Bec56] Edwin Ford Beckenbach, editor. Modern Mathematics for the Engineer: First Series. University of California Engineering Extension Series. McGraw-Hill, New York, NY, USA, 1956. xxii + 514 pp.

Beckenbach:1962:MME

[Bec62] Edwin Ford Beckenbach, editor. Modern Mathematics for the Engineer: Second Series. McGraw-Hill, New York, NY, USA, 1962. xviii + 456 pp. LCCN QA401 .B4. With an introduction by Magnus R. Hestenes.

Beckenbach:2013:MMEa

[Bec13a] Edwin Ford Beckenbach, editor. Modern Mathematics for the Engineer: First Series. Dover books on engineering. Dover, New York, NY, USA, 2013. ISBN 0-486-49746-1 (paperback), 0-486-31611-4 (e-book). xx + 514 pp. LCCN QA401 .B4 2013. With an introduction by Royal Weller. Reprint of [Bec56].

Beckenbach:2013:MMEb

[Bec13b] Edwin Ford Beckenbach, editor. Modern Mathematics for the Engineer: Second Series. Dover, New York, NY, USA, 2013. ISBN 0-486-31612-2 (e-book), 0-486-49747-X (paperback), 1-306-32668-0 (e-book). xviii + 456 pp. LCCN QA401 .B39 2013. With an introduction by Magnus R. Hestenes. Reprint of [Bec62].

Berkovitz:1992:MMR

[Ber92] Leonard D. Berkovitz. In memory of Magnus R. Hestenes. Journal of Optimization Theory and Applications, 73(2):225–227, May 1992. CODEN JOTABN. ISSN 0022-3239 (print), 1573-2878 (electronic).

Bader:1981:QHT

[BF81] Laura Bader and Anna Franchetta.

Quasiprimitive Hestenes ternary rings. Rendiconti di Matematica. Serie VII, 1(3):411–430, 1981. ISSN 0034-4427.

Bonettini:2004:HMS

[BGR04] S. Bonettini, E. Galligani, and V. Ruggiero. Hestenes method for symmetric indefinite systems in interior-point method. Rendiconti di matematica e delle sue applicazioni (1981), 24(1):185– 199, 2004. CODEN RNMTAN. ISSN 1120-7183. URL https://

doaj.org/toc/2532-3350.

Bonettini:2005:INM

[BGR05] Silvia Bonettini, Emanuele Galligani, and Valeria Ruggiero. An inexact Newton method combined with Hestenes multipliers’ scheme for the solution of Karush–Kuhn–Tucker systems. Applied Mathematics and Computation, 168(1):651– 676, September 1, 2005. CO-DEN AMHCBQ. ISSN 0096-3003 (print), 1873-5649 (elec-

tronic).  URL http://www.
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Bliss:1932:SCP

[BH32] G. A. Bliss and M. R. Hestenes. Sufficient conditions for a problem of Mayer in the calculus of variations. Bulletin of the American Mathematical Society, 38(5):347–348, May 1932. CO-DEN BAMOAD. ISSN 0002-9904 (print), 1936-881x (elec-

                                        tronic). URL https://www.ams.
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                                        05/S0002-9904-1932-05405-2/
                                        S0002-9904-1932-05405-2.pdf.

Bliss:1933:NPB

[BH33a] G. A. Bliss and M. R. Hestenes. A note on the problem of Bolza in the calculus of variations. Bulletin of the American Mathematical Society, 39(5):341, May 1933. CODEN BAMOAD. ISSN 0002-9904 (print), 1936-881x (elec-

                                        tronic). URL https://www.ams.
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                                        05/S0002-9904-1933-05620-3/
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Bliss:1933:SCP

[BH33b] G. A. Bliss and M. R. Hestenes. Sufficient conditions for a problem of Mayer in the calculus of variations. In Contributions to the Calculus of Variations 1931– 1932 [Hes33e], pages 295–337.

Birkhoff:1935:GMPa

[BH35a] G. D. Birkhoff and M. R. Hestenes. Generalized minimax principle in the calculus of variations. Proceedings of the National Academy of Sciences of the United States of America, 21 (2):96–99, February 1935. CO-DEN PNASA6. ISSN 0027-8424 (print), 1091-6490 (electronic).

Birkhoff:1935:GMPb

[BH35b] G. D. Birkhoff and M. R.

Hestenes. Generalized minimax principle in the calculus of variations. Duke Mathematical Journal, 1(4):413–432, December 1935. CODEN DUMJAO. ISSN 0012-7094 (print), 1547-7398 (electronic).

Birkhoff:1935:NICa

[BH35c] G. D. Birkhoff and M. R.

Hestenes. Natural isoperimetric conditions in the calculus of variations. Proceedings of the National Academy of Sciences of the United States of America, 21 (2):99–102, February 1935. CO-DEN PNASA6. ISSN 0027-8424 (print), 1091-6490 (electronic).

Birkhoff:1935:NICb

[BH35d] G. D. Birkhoff and M. R.

Hestenes. Natural isoperimetric conditions in the calculus of variations. Duke Mathematical Journal, 1(2), June 1935. CO-DEN DUMJAO. ISSN 0012-7094 (print), 1547-7398 (electronic).

Ben-Israel:1964:DSD

[BI64] Adi Ben-Israel. On direct sum decompositions of Hestenes algebras. Israel Journal of Mathematics, 2:50–54, March 1964. CO-DEN ISJMAP. ISSN 0021-2172 (print), 1565-8511 (electronic).

Babaie-Kafaki:2015:HHS

[BKG15] Saman Babaie-Kafaki and Reza Ghanbari. A hybridization of the Hestenes–Stiefel and Dai– Yuan conjugate gradient methods based on a least-squares approach. Optimization Methods and Software, 30(4):673–681, October 2015. ISSN 1026-7670 (print), 1055-6788 (electronic).

Babaie-Kafaki:2017:EHS

[BKG17] S. Babaie-Kafaki and R. Ghanbari. Extensions of the Hestenes– Stiefel and Polak–Ribière–Polyak conjugate gradient methods with sufficient descent property. Bulletin of the Iranian Mathematical Society, 43(7):2437–2448, 2017. ISSN 1017-060X. URL https:

//www.springer.com/journal/
41980.

Babaie-Kafaki:2018:LHH

[BKG18] Saman Babaie-Kafaki and Reza Ghanbari. A linear hybridization of the Hestenes–Stiefel method and the memoryless BFGS technique. Mediterranean Journal of Mathematics, 15(3):Paper No. 86, 10, April 2018. ISSN 1660-5446 (print), 1660-5454 (electronic).

Bolza:1901:NPT

[Bol01] Oskar Bolza. New proof of a theorem of Osgood’s in the calculus of variations. Transactions of the American Mathematical Society, 2(4):422–427, October 1901. CO-DEN TAMTAM. ISSN 0002-9947 (print), 1088-6850 (electronic).

URL https://en.wikipedia.
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Bartolozzi:1977:ATH

[BP77] Federico Bartolozzi and Gianfranco Panella. Anelli ternari di Hestenes semplici, artiniani e privi di ideali bilateri effettivi. Ricerche di Matematica (Napoli), 26(2):255–275, 1977. CODEN RCMTAE. ISSN 0035-5038 (print), 1827-3491 (electronic).

Baluch:2018:NMT

[BSA18] Bakhtawar Baluch, Zabidin Salleh, and Ahmad Alhawarat. A new modified three-term Hestenes–Stiefel conjugate gradient method with sufficient descent property and its global convergence. Journal of Optimization, 2018:Art. ID 5057096, 13, September 2018. ISSN 2314-6486 (print), 2356-752X (electronic).

Bukovices:1967:BRM

[Buk67] E. Bukovices. Book report: M.

R. Hestenes, Calculus of Variations and Optimal Control Theory. Computing: Archiv für Informatik und Numerik, 2(4): 374, December 1967. CODEN CMPTA2. ISSN 0010-485X (print), 1436-5057 (electronic).

Caggegi:1980:SHT

[Cag80] Andrea Caggegi. Simple Hestenes ternary rings, right Artinian and with no effective two-sided ideals. Rendiconti di Matematica. Serie VI., 13(1):85–103, 1980. ISSN 0034-4427.

Caggegi:1981:PHT

[Cag81]  Andrea Caggegi.  Primitive

Hestenes ternary rings with minimal right ideal. Annali di matematica pura ed applicata. Series 4, 128(1):169–191, December 1981. CODEN ANLMAE. ISSN 0003-4622.

Chernov:1997:HFD

[CC97] A. V. Chernov and V. M. Chernov. On Hestenes’ formalization for describing linear image transforms. Lecture Notes in Computer Science, 1315:164– 175, 1997. CODEN LNCSD9. ISSN 0302-9743 (print), 1611-3349 (electronic).

Chan:1991:MH

[Cha91] Tony Chan. Magnus Hestenes. Netlib Web site., June 4,

                                        1991.  URL https://www.
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                                        91/v91n24.html#2.

Carson:2024:TUC

[CLS24] Erin Carson, Jörg Liesen, and Zdeněk Strakoš. Towards understanding CG and GMRES through examples. Linear Algebra and its Applications, 692 (??):241–291, July 1, 2024. CO-DEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (elec-

                                        tronic).  URL http://www.
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Cuomo:2018:PIH

[CMN18] Salvatore Cuomo, Livia Marcellino, and Guglielmo Navarra. A parallel implementation of the Hestenes–Jacobi-one-sides method using GPU-CUDA. In 2018 26th Euromicro International Conference on Parallel, Distributed and Network-based Processing (PDP), pages 722– 725. IEEE Computer Society Press, 1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA, 2018.

Crane:1987:HAC

[Cra87] G. E. Crane, editor. HSNC’87:

ACM Conference on the History of Scientific and Numeric Computation, conference proceedings: papers presented at the Conference, Princeton, New Jersey, May 13-15, 1987. ACM Press, New York, NY 10036, USA, October 1987. ISBN 0-89791-229-2. LCCN QA76 .A25 1987.

Cullum:1977:BRO

[Cul77] Jane Cullum. Book review: Optimization Theory; The Finite Dimensional Case (Magnus R. Hestenes). SIAM Review, 19(4): 750–752, October 1977. CO-DEN SIREAD. ISSN 0036-1445 (print), 1095-7200 (electronic).

Dai:2005:MHS

[DC05] Zhi Feng Dai and Lan Ping Chen.

A mixed Hestenes–Stiefel Dan– Yuan conjugate gradient method. Mathematica Numerica Sinica. Jisuan Shuxue, 27(4):429–436, 2005. ISSN 0254-7791.

Deal:1964:BRM

[Dea64] Roy B. Deal. Book review: Modern Mathematics for the Engineer, Edited by Edwin F. Beckenbach. New York, McGraw-Hill, 1956. xxii + 514 pp. Pi Mu Epsilon Journal, 4(1):22, Fall 1964. CODEN PMEJBR. ISSN 0031-952X. URL https://www.

jstor.org/stable/24339253.

Dong:2017:SNT

[DHG^{+}17] Xiao-Liang Dong, De-Ren Han, Reza Ghanbari, Xiang-Li Li, and Zhi-Feng Dai. Some new threeterm Hestenes–Stiefel conjugate gradient methods with affine combination. Optimization, 66 (5):759–776, February 2017. CO-DEN OPTZDQ. ISSN 0233-1934, 0323-3898.

Dong:2015:MHS

[DLHY15] Xiao Liang Dong, Hong Wei Liu, Yu Bo He, and Xi Mei Yang. A modified Hestenes–Stiefel conjugate gradient method with sufficient descent condition and conjugacy condition. Journal of Computational and Applied Mathematics, 281(??): 239–249, June 2015. CO-DEN JCAMDI. ISSN 0377-0427 (print), 1879-1778 (elec-

tronic).  URL http://www.
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Dong:2017:MNH

[DLL^{+}17] Xiao-Liang Dong, Hong-Wei Liu, Xiang-Li Li, Yu-Bo He, and Ze-Xian Liu. A modified nonmonotone Hestenes–Stiefel type conjugate gradient methods for large-scale unconstrained problems. Numerical Functional Analysis and Optimization, 38 (1):39–50, September 2017. CO-DEN NFAODL. ISSN 0163-0563 (print), 1532-2467 (electronic).

Dong:2019:EAT

[DLLL19] Xiao-Liang Dong, Ze-Xian Liu, Hong-Wei Liu, and Xiang-Li Li. An efficient adaptive three-term extension of the Hestenes–Stiefel conjugate gradient method. Optimization Methods and Software, 34(3):546–559, October 2019. ISSN 1026-7670 (print), 1055-6788 (electronic).

Dreyfus:1965:BRC

[Dre65] S. E. Dreyfus. Book review:

Computing methods in optimization problems, A. V. Balakrishnan and Lucien W. Neustadt. Quarterly of Applied Mathematics, 23(3):264, 1965. CO-DEN QAMAAY. ISSN 0033-569X (print), 1552-4485 (elec-

tronic).  URL http://www.
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Dongarra:2000:GEI

[DS00] Jack Dongarra and Francis Sullivan. Guest Editors’ introduction: The top 10 algorithms. Computing in Science and Engineering, 2(1):22–23, January/February 2000. CODEN CSENFA. ISSN 1521-9615 (print), 1558-366X (electronic). URL http://

dlib.computer.org/cs/books/
cs2000/pdf/c1022.pdf;   http:
//www.computer.org/cse/cs1999/

c1022abs.htm. See correspondence [?].

Durazzi:1999:NSD

[Dur99] Carla Durazzi. Numerical solution of discrete quadratic optimal control problems by Hestenes’ method. Rendiconti del Circolo Matematico di Palermo. Serie II. Supplemento, 58:133–154, 1999. ISSN 1592-9531. Proceedings of the Workshop “Numerical Methods in Optimization” (Cortona, 1997)”.

Dai:2012:GCM

[DW12] Zhifeng Dai and Fenghua Wen. Global convergence of a modified Hestenes–Stiefel nonlinear conjugate gradient method with Armijo line search. Numerical Algorithms, 59(1):79–93, January 2012. CODEN NUALEG. ISSN 1017-1398 (print), 1572-9265 (electronic). URL http://www.

                                        springerlink.com/openurl.asp?
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Faramarzi:2021:STT

[FA21] Parvaneh Faramarzi and Keyvan Amini. A spectral three-term Hestenes–Stiefel conjugate gradient method. 4OR, 19(1):71–92, February 2021. ISSN 1614-2411 (print), 1619-4500 (electronic).

Forsythe:1951:IMS

[FHR51] George E. Forsythe, Magnus R. Hestenes, and J. Barkley Rosser. Iterative methods for solving linear equations. Bulletin of the American Mathematical Society, 57(6):480, November 1951. CO-DEN BAMOAD. ISSN 0002-9904 (print), 1936-881X (elec-

tronic). URL https://www.
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57-06/.

Fox:1948:NSA

[FHW48] L. Fox, H. D. Huskey, and J. H.

Wilkinson. Notes on the solution of algebraic linear simultaneous equations. Quarterly Journal of Mechanics and Applied Mathematics, 1:149–173, 1948. CO-DEN QJMMAV. ISSN 0033-5614 (print), 1464-3855 (electronic).

Fortin:1975:MSN

[For75] Michel Fortin. Minimization of some non-differentiable functionals by the augmented Lagrangian method of Hestenes and Powell. Applied Mathematics and Optimization, 2(3):236–250, September 1975. CODEN AMOMBN. ISSN 0095-4616 (print), 1432-0606 (electronic).

Friedman:1973:RTM

[Fri73]  Kenneth Friedman.  Replies

to Tribus and Motroni and to Gage and Hestenes. Journal of Statistical Physics, 9 (3):265–269, November 1973. CODEN JSTPSB. ISSN 0022-4715 (print), 1572-9613 (electronic). URL http://

link.springer.com/article/
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Ferrarotti:1998:GHLa

[FW98a] Massimo Ferrarotti and Leslie C.

Wilson. Generalized Hestenes lemma and extension of functions. In Geometry Seminars, 1996–1997 (Italian) (Bologna), pages 99–109. Università degli Studi di Bologna, Dipartimento di Matematica, Bologna, Italy, 1998.

Ferrarotti:1998:GHLb

[FW98b] Massimo Ferrarotti and Leslie C. Wilson. Generalized Hestenes’ lemma and extension of functions. Transactions of the American Mathematical Society, 350 (5):1957–1975, May 1998. CO-DEN TAMTAM. ISSN 0002-9947 (print), 1088-6850 (electronic).

Ferrarotti:2008:RGH

[FW08] Massimo Ferrarotti and Leslie C. Wilson. Remarks on the generalized Hestenes’s lemma. Rocky Mountain Journal of Mathematics, 38(2):461–469, April 2008. CODEN RMJMAE. ISSN 0035-7596 (print), 1945-3795 (electronic).

Golub:1989:SHC

[GO89] Gene H. Golub and Dianne P. O’Leary. Some history of the conjugate gradient and Lanczos algorithms: 1948–1976. SIAM Review, 31(1):50–102, March 1989. CODEN SIREAD. ISSN 0036-1445 (print), 1095-7200 (elec-

                                        tronic).  URL http://www.
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Guinn:1965:PBS

[Gui65a] T. Guinn. The problem of bounded space coordinates as a problem of Hestenes. Journal of the Society for Industrial and Applied Mathematics. Series A, On control, 3(2):181–190, January 1965. CODEN JSMCAL. ISSN 0887-4603 (print), 2168-359X (electronic).

Guinn:1965:WHV

[Gui65b] T. Guinn. Weakened hypotheses for the variational problem considered by Hestenes. Journal of the Society for Industrial and Applied Mathematics. Series A, On control, 3(3):418–423, January 1965. CODEN JSMCAL. ISSN 0887-4603 (print), 2168-359X (electronic).

Guo:1995:GCH

[GXS95] Wen Ying Guo, Da Chuan Xu, and Gui Cheng Shen. Global convergence of the Hestenes–Stiefel conjugate gradient method. Kexue Tongbao (Chinese), 40 (23):2113–2117, 1995. ISSN 0023-074X (print), 2095-9419 (electronic).

Halil:2021:MHS

[HAE21] Isam H. Halil, Khalil K. Abbo, and Hassan H. Ebrahim. Modifications of Hestenes and Stiefel CG method for solving unconstrained optimization problems. In 2021 7th International Conference on Contemporary Information Technology and Mathematics (ICCITM), pages 274–278. IEEE Computer Society Press, 1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA, 2021.

Hansen:1988:RNS

[Han88] P. C. Hansen. Reducing the number of sweeps in Hestenes method. In E. F. Deprettere, editor, Singular Value Decomposition and Signal Processing. North-Holland Publishing Co., Amsterdam, The Netherlands, 1988.

Hestenes:1933:SCPa

[HB33] M. R. Hestenes and G. A. Bliss. Sufficient conditions for a problem of Mayer in the calculus of variations. Transactions of the American Mathematical Society, 35(1):305–326, January 1933. CODEN TAMTAM. ISSN 0002-9947 (print), 1088-6850 (electronic).

Hegedus:1987:GRHb

[Heg88a] Cs. J. Hegedűs. General recursions of Hestenes–Stiefel type for conjugate directions. II. The reverse recursion. Alkalmazott Matematikai Lapok, 13(3–4):361– 372, 1987/88. ISSN 0133-3399.

Hegedus:1987:GRHa

[Heg88b] Csaba J. Hegedűs. General recursions of Hestenes–Stiefel type for conjugate directions. I. The direct recursion. Alkalmazott Matematikai Lapok, 13(1–2):83– 96, 1987/88. ISSN 0133-3399.

Hestenes:1928:PRS

[Hes28] Magnus Rudolph Hestenes. Path of a rotating sphere. M.A. thesis, University of Wisconsin-Madison, Madison, WI, USA, 1928. 160 pp. URL https:/

                                        /books.google.com/books?id=
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Hestenes:1931:SCG

[Hes31] M. R. Hestenes. Sufficient conditions for the general problem of Mayer with variable endpoints. In Contributions to the Calculus of Variations 1931–1932 [Hes33e], pages 339–359.

Hestenes:1932:SCP

[Hes32a] M. R. Hestenes. Sufficient conditions for a problem of Mayer with variable endpoints. Bulletin of the American Mathematical Society, 38(5):348, May 1932. CODEN BAMOAD. ISSN 0002-9904 (print), 1936-881x (elec-

tronic). URL https://www.ams.
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Hestenes:1932:SCG

[Hes32b] Magnus Rudolf Hestenes. Sufficient Conditions for the General Problem of Mayer with Variable End-Points. Ph.D. dissertation, Department of Mathematics, University of Chicago, Chicago, IL, USA, June 1932. iii + 19 pp. URL http://pi.

lib.uchicago.edu/1001/cat/
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Hestenes:1933:NJC

[Hes33a] M. R. Hestenes. A note on the Jacobi condition for parametric problems in the calculus of variations. Bulletin of the American Mathematical Society, 39(7):509, July 1933. CO-DEN BAMOAD. ISSN 0002-9904 (print), 1936-881x (elec-

                                        tronic). URL https://www.ams.
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Hestenes:1933:SCG

[Hes33b] M. R. Hestenes. Sufficient conditions for the general problem of Mayer with variable end points. Transactions of the American Mathematical Society, 35(2):479– 490, April 1933. CODEN TAM-TAM. ISSN 0002-9947 (print), 1088-6850 (electronic).

Hestenes:1933:SCPc

[Hes33c] M. R. Hestenes. Sufficient conditions for the problem of Bolza in the calculus of variations. Bulletin of the American Mathematical Society, 39(7):506, July 1933. CODEN BAMOAD. ISSN 0002-9904 (print), 1936-881x (elec-

                                        tronic). URL https://www.ams.
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                                        07/S0002-9904-1933-05674-4/
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Hestenes:1933:SCPb

[Hes33d] M. R. Hestenes. Sufficient conditions for the problem of Lagrange in the calculus of variations. Bulletin of the American Mathematical Society, 39(5):341, May 1933. CODEN BAMOAD. ISSN 0002-9904 (print), 1936-881x (elec-

                                        tronic). URL https://www.ams.
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Hestenes:1933:CCV

[Hes33e] Magnus R. Hestenes. Contributions to the Calculus of Variations 1931–1932. University of Chicago Press, Chicago, IL, USA, 1933. vii + 523 pp.

Hestenes:1934:BTP

[Hes34a] M. R. Hestenes. A basis theorem in the problems of Lagrange and Bolza. Bulletin of the American Mathematical Society, 40(11):802–803, November 1934. CODEN BAMOAD. ISSN 0002-9904 (print), 1936-881x (elec-

tronic). URL https://www.ams.
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Hestenes:1934:NJC

[Hes34b] M. R. Hestenes. A note on the Jacobi condition for parametric problems in the calculus of variations. Bulletin of the American Mathematical Society, 40 (4):297–302, April 1934. CO-DEN BAMOAD. ISSN 0002-9904 (print), 1936-881x (elec-

tronic). URL https://www.ams.
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Hestenes:1934:PBC

[Hes34c] M. R. Hestenes. The problem of Bolza in the calculus of variations in parametric form. Bulletin of the American Mathematical Society, 40(9):657, September 1934.

CODEN BAMOAD. ISSN 0002-9904 (print), 1936-881x (elec-

tronic). URL https://www.ams.
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Hestenes:1934:SCPa

[Hes34d] M. R. Hestenes. Sufficient conditions for the problem of Bolza in the calculus of variations. Transactions of the American Mathematical Society, 36(4):793–818, October 1934. CODEN TAM-TAM. ISSN 0002-9947 (print), 1088-6850 (electronic).

Hestenes:1934:SCPb

[Hes34e] M. R. Hestenes. Sufficient conditions for the problem of Bolza in the calculus of variations. II. Bulletin of the American Mathematical Society, 40 (3):220, March 1934. CO-DEN BAMOAD. ISSN 0002-9904 (print), 1936-881x (elec-

tronic). URL https://www.ams.
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Hestenes:1936:MPF

[Hes36a] M. R. Hestenes. Minimax principle for functions. Proceedings of the National Academy of Sciences of the United States of America, 22(2):115–119, February 1936. CODEN PNASA6. ISSN 0027-8424 (print), 1091-6490 (electronic). URL https:

//www.pnas.org/doi/10.1073/
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Hestenes:1936:SCP

[Hes36b] Magnus R. Hestenes. On sufficient conditions in the problems of Lagrange and Bolza. Annals of Mathematics (2), 37(3):543– 551, July 1936. CODEN AN-MAAH. ISSN 0003-486x (print), 1939-8980 (electronic).

Hestenes:1936:PBC

[Hes36c] Magnus R. Hestenes. The problem of Bolza in the calculus of variations in parametric form. American Journal of Mathematics, 58(2):391–406, April 1936. CODEN AJMAAN. ISSN 0002-9327 (print), 1080-6377 (electronic).

Hestenes:1937:DSP

[Hes37] Magnus R. Hestenes. A direct sufficiency proof for the problem of Bolza in the calculus of variations. Transactions of the American Mathematical Society, 42(1):141–154, July 1937. CO-DEN TAMTAM. ISSN 0002-9947 (print), 1088-6850 (electronic).

Hestenes:1938:SPI

[Hes38] M. H. Hestenes. A sufficiency proof for isoperimetric problems in the calculus of variations. Bulletin of the American Mathematical Society, 44(10):662–667, October 1938. CODEN BAMOAD. ISSN 0002-9904 (print), 1936-881X (electronic). URL https:/

/www.ams.org/journals/bull/
1938-44-10/S0002-9904-1938-
06838-3/.

Hestenes:1939:GPB

[Hes39] M. R. Hestenes. Generalized problem of Bolza in the calculus of variations. Duke Mathematical Journal, 5(2):309–324, June 1939. CODEN DUMJAO. ISSN 0012-7094 (print), 1547-7398 (electronic).

Hestenes:1941:ERD

[Hes41a] M. R. Hestenes. Extension of the range of a differentiable function. Duke Mathematical Journal, 8 (1):183–192, March 1941. CO-DEN DUMJAO. ISSN 0012-7094 (print), 1547-7398 (electronic).

Hestenes:1941:AGT

[Hes41b] Magnus R. Hestenes. An analogue of Green’s theorem in the calculus of variations. Duke Mathematical Journal, 8(2):300– 311, June 1941. CODEN DUM-JAO. ISSN 0012-7094 (print), 1547-7398 (electronic).

Hestenes:1942:PBC

[Hes42] M. R. Hestenes. The problem of Bolza in the calculus of variations. Bulletin of the American Mathematical Society, 48 (2):57–75, February 1942. CO-DEN BAMOAD. ISSN 0002-9904 (print), 1936-881x (elec-

                                        tronic). URL https://www.ams.
                                        org/journals/bull/1942-48-
                                        02/S0002-9904-1942-07600-2/
                                        S0002-9904-1942-07600-2.pdf.

Hestenes:1945:TCP

[Hes45] Magnus R. Hestenes. A theory of critical points. American Journal of Mathematics, 67(4):521– 562, October 1945. CODEN AJ-MAAN. ISSN 0002-9327 (print), 1080-6377 (electronic).

Hestenes:1946:SCI

[Hes46a] Magnus R. Hestenes. Sufficient conditions for the isoperimetric problem of Bolza in the calculus of variations. Transactions of the American Mathematical Society, 60(1):93–118, July 1946. CO-DEN TAMTAM. ISSN 0002-9947 (print), 1088-6850 (electronic).

Hestenes:1946:TLC

[Hes46b] Magnus R. Hestenes. Theorem of Lindeberg in the calculus of variations. Transactions of the American Mathematical Society, 60(1): 72–92, July 1946. CODEN TAM-TAM. ISSN 0002-9947 (print), 1088-6850 (electronic).

Hestenes:1946:WFC

[Hes46c] Magnus R. Hestenes. The Weierstrass E-function in the calculus of variations. Transactions of the American Mathematical Society, 60(1):51–71, July 1946. CO-DEN TAMTAM. ISSN 0002-9947 (print), 1088-6850 (electronic).

Hestenes:1947:ASP

[Hes47a] Magnus R. Hestenes. An alternate sufficiency proof for the normal problem of Bolza. Transactions of the American Mathematical Society, 61(2):256–264, March 1947. CODEN TAM-TAM. ISSN 0002-9947 (print), 1088-6850 (electronic).

Hestenes:1947:ISP

[Hes47b] Magnus R. Hestenes. An indirect sufficiency proof for the problem of Bolza in nonparametric form. Transactions of the American Mathematical Society, 62(3): 509–535, November 1947. CO-DEN TAMTAM. ISSN 0002-9947 (print), 1088-6850 (electronic).

Hestenes:1948:SCM

[Hes48] Magnus R. Hestenes. Sufficient conditions for multiple integral problems in the calculus of variations. American Journal of Mathematics, 70(2):239– 276, April 1948. CODEN AJ-MAAN. ISSN 0002-9327 (print), 1080-6377 (electronic).

Hestenes:1949:NMO

[Hes49] Magnus Rudolph Hestenes. Numerical methods of obtaining solutions of fixed endpoint problems in the calculus of variations. Research Memorandum RM-0102-PR, The RAND Corporation, Santa Monica, CA, USA, 1949. 17 pp. URL https://

www.rand.org/pubs/research_
memoranda/RM0102.html.

Hestenes:1950:EIC

[Hes50a] Magnus R. Hestenes. An elementary introduction to the calculus of variations. Mathematics Magazine, 23(5):249–267, May/ June 1950. CODEN MAMGA8. ISSN 0025-570X (print), 1930-0980 (electronic). URL https:

//www.jstor.org/stable/pdf/
3028990.pdf.

Hestenes:1950:GPC

[Hes50b] Magnus Rudolph Hestenes. A general problem in the calculus of variations with applications to the paths of least time. Research Memorandum RM-100, The RAND Corporation, Santa Monica, CA, USA, March 1, 1950. i + 45 pp. URL https://

www.rand.org/pubs/research_
memoranda/RM100.html.

Hestenes:1951:ATQ

[Hes51a] Magnus R. Hestenes. Applications of the theory of quadratic forms in Hilbert space to the calculus of variations. Pacific Journal of Mathematics, 1(4): 525–581, December 1951. CO-DEN PJMAAI. ISSN 0030-8730 (print), 1945-5844 (electronic).

URL http://projecteuclid.
org/euclid.pjm/1103052021.

Entry [Mie74] says this is perhaps Hestenes’s best known paper, although the conjugate gradient paper [HS52] is also highly cited.

Hestenes:1951:IMS

[Hes51b] Magnus R. Hestenes. Iterative methods for solving linear equations. NAML Report 52-9, National Bureau of Standards, Los Angeles, CA, USA, July 2, 1951.

Hestenes:1953:DEE

[Hes53] Magnus R. Hestenes. Determination of eigenvalues and eigenvectors of matrices. In Paige and Taussky [PT53], pages 89– 94. LCCN QA3 .U5 no. 29.

Hestenes:1954:HSM

[Hes54] Magnus R. Hestenes. Hilbert space methods in variational theory and numerical analysis. In J. Gerretsen and J. De Groot, editors, Proceedings of the International Congress of Mathematicians 1954. Amsterdam, September 2–9. Vol. III. Stated addresses in sections. Symposia, volume 3, pages 229–236. North-Holland Publishing Co., Amsterdam, The Netherlands, 1954.

Hestenes:1955:ICM

[Hes55] Magnus R. Hestenes. Iterative computational methods. Communications on Pure and Applied Mathematics (New York), 8(1): 85–96, February 1955. CODEN CPAMAT, CPMAMV. ISSN 0010-3640 (print), 1097-0312 (electronic).

Hestenes:1956:CGM

[Hes56a] Magnus R. Hestenes. The conjugate gradient method for solving linear systems. In Proceedings of Symposia in Applied Mathematics. Vol. VI, Numerical analysis, pages 83–102. McGraw-Hill, New York, NY, USA, 1956.

Hestenes:1956:ECV

[Hes56b] Magnus R. Hestenes. Elements of the calculus of variations. In Beckenbach [Bec56], chapter 4, page ??

Hestenes:1958:IMB

[Hes58] Magnus R. Hestenes. Inversion of matrices by biorthogonalization and related results. Journal of the Society for Industrial and Applied Mathematics, 6(1): 51–90, March 1958. CODEN JSI-MAV. ISSN 0368-4245 (print), 1095-712X (electronic).

Hestenes:1961:RHM

[Hes61a] M. R. Hestenes. Relative Hermitian matrices. Pacific Journal of Mathematics, 11(1):225– 245, March 1961. CODEN PJ-MAAI. ISSN 0030-8730 (print), 1945-5844 (electronic).

Hestenes:1961:QVT

[Hes61b] Magnus R. Hestenes. Quadratic variational theory and linear elliptic partial differential equations. Transactions of the American Mathematical Society, 101 (2):306–350, November 1961. CODEN TAMTAM. ISSN 0002-9947 (print), 1088-6850 (electronic).

Hestenes:1961:RSA

[Hes61c] Magnus R. Hestenes. Relative self-adjoint operators in Hilbert space. Pacific Journal of Mathematics, 11(4):1315–1357, December 1961. CODEN PJMAAI. ISSN 0030-8730 (print), 1945-5844 (electronic). URL http:

//projecteuclid.org/euclid.
pjm/1103036917.

Hestenes:1962:I

[Hes62a] Magnus R. Hestenes. Introduction. In Beckenbach [Bec62], page ???? LCCN QA401 .B4. With an introduction by Magnus R. Hestenes.

Hestenes:2013:I

[Hes62b] Magnus R. Hestenes. Introduction. In Beckenbach [Bec13b], page ???? ISBN 0-486-31612-2 (e-book), 0-486-49747-X (paperback), 1-306-32668-0 (e-book). LCCN QA401 .B39 2013. With an introduction by Magnus R. Hestenes. Reprint of [Bec62].

Hestenes:1962:TAA

[Hes62c] Magnus R. Hestenes. A ternary algebra with applications to matrices and linear transformations. Archive for Rational Mechanics and Analysis, 11(1):138–195, January 1962. CODEN AVR-MAW. ISSN 0003-9527 (print), 1432-0673 (electronic). URL

                                        https://link.springer.com/
                                        article/10.1007/BF00253936.

Hestenes:1964:VTO

[Hes64] Magnus R. Hestenes. Variational theory and optimal control theory. In A. V. Balakrishnan and Lucien W. Neustadt, editors, Computational Methods in Optimization Problems, Proceedings of a conference held at University of California, Los Angeles, January 30–31, 1964, pages 1–22. Academic Press, New York, USA, 1964.

Hestenes:1965:VTO

[Hes65] Magnus R. Hestenes. On variational theory and optimal control theory. Journal of the Society for Industrial and Applied Mathematics. Series A, On control, 3 (1):23–48, January 1965. CO-DEN JSMCAL. ISSN 0887-4603 (print), 2168-359X (electronic).

Hestenes:1966:ECV

[Hes66a] M. R. Hestenes. Elements of calculus of variations and optimum control theory. In J. Barkley Rosser, editor, Lectures in Applied Mathematics VI, Space Mathematics. Part 2, Proceedings of the Summer Seminar, Ithaca, New York, 1963, volume 6 of Lectures in Applied Mathematics, pages 212–254. American Mathematical Society, Providence, RI, USA, 1966.

Hestenes:1966:CVO

[Hes66b] Magnus R. Hestenes. Calculus of Variations and Optimal Control Theory. Wiley, New York, NY, USA, 1966. ISBN 0-471-37470-9. xii + 405 pp.

Hestenes:1968:PQF

[Hes68] Magnus R. Hestenes. Pairs of quadratic forms. Linear Algebra and its Applications, 1 (3):397–407, July 1968. CO-DEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (elec-

tronic).  URL http://www.
sciencedirect.com/science/
article/pii/0024379568900165.

Hestenes:1969:MGMa

[Hes69a] M. R. Hestenes. Multiplier and gradient methods. In Zadeh et al. [ZNB69], pages 143–163. LCCN QA402.5 .I5 1968.

Hestenes:1969:MGMb

[Hes69b] Magnus R. Hestenes. Multiplier and gradient methods. Journal of Optimization Theory and Applications, 4(5):303–320, November 1969. CODEN JOTABN. ISSN 0022-3239 (print), 1573-2878 (electronic).

Hestenes:1969:VTO

[Hes69c] Magnus R. Hestenes. Variational theory and optimal control theory. In Zadeh et al. [ZNB69], page ?? LCCN QA402.5 .I5 1968.

Hestenes:1973:IMS

[Hes73a] M. R. Hestenes. Iterative methods for solving linear equations. Journal of Optimization Theory and Applications, 11(4):323–334, April 1973. CODEN JOTABN. ISSN 0022-3239 (print), 1573-2878 (electronic).

Hestenes:1973:TA

[Hes73b] Magnus R. Hestenes. On a ternary algebra. Scripta Mathematica, 29(3–4):253–272, 1973. ISSN 0036-9713.

Hestenes:1975:QCP

[Hes75a] M. R. Hestenes. Quadratic control problems. Journal of Optimization Theory and Applications, 17(1–2):1–42, October 1975. CODEN JOTABN. ISSN 0022-3239 (print), 1573-2878 (electronic).

Hestenes:1975:OTF

[Hes75b] Magnus R. Hestenes. Optimization Theory: The Finite Dimensional Case. Wiley, New York, NY, USA, 1975. ISBN 0-471-37471-7 (hardcover). xiii + 447 pp. LCCN QA402.5 .H47.

Hestenes:1975:PCG

[Hes75c] Magnus R. Hestenes. Pseudoinverses and conjugate gradients. Communications of the ACM, 18 (1):40–43, January 1975. CO-DEN CACMA2. ISSN 0001-0782 (print), 1557-7317 (electronic). Collection of articles honoring Alston S. Householder.

Hestenes:1976:QCP

[Hes76a] Magnus R. Hestenes. On quadratic control problems. In Russell [Rus76], pages 289–304. ISBN 0-12-604150-4. LCCN QA3 .U45 no. 36 QA315; QA402.3. Publication number 36.

Hestenes:1976:RPA

[Hes76b] Magnus R. Hestenes. A role of the pseudoinverse in analysis. In M. Zuhair Nashed, editor, Generalized Inverses and Applications. Proceedings of an Advanced Seminar sponsored by the Mathematics Research Center at the University of Wisconsin, Madison, Wisconsin, October 8–10, 1973, pages 175–192. Academic Press, New York, USA, 1976. Publication number 32.

Hestenes:1978:CDM

[Hes78a] Magnus R. Hestenes. Conjugate direction methods in optimization. In J. Stoer, editor, Optimization Techniques. Part 1. Proceedings of the 8th IFIP Conference on Optimization Techniques held in Würzburg, September 5–9, 1977, volume 6 of Lecture Notes in Control and Information Sciences, pages 8– 27. Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 1978. ISBN 3-540-08707-9.

Hestenes:1978:SOP

[Hes78b] Magnus R. Hestenes. Solving optimization problems. In A. B. Schwarzkopf, Walter G. Kelley, and Stanley B. Eliason, editors, Optimal Control and Differential Equations. Proceedings of the Conference on Optimal Control and Differential Equations held at the University of Oklahoma, Norman, Oklahoma, March 24– 27, 1977, pages 165–185. Academic Press, New York, USA, 1978. ISBN 0-12-632250-3.

Hestenes:1980:AOT

[Hes80a] M. R. Hestenes. Augmentability in optimization theory. Journal of Optimization Theory and Applications, 32(4):427–440, December 1980. CODEN JOTABN. ISSN 0022-3239 (print), 1573-2878 (electronic).

Hestenes:1980:CVO

[Hes80b] Magnus R. Hestenes. Calculus of Variations and Optimal Control Theory. Applied Mathematics Series. Robert E. Krieger Publishing Company, Huntington, NY, USA, 1980. ISBN 0-471-37470-9. xii + 405 pp. Reprint of [Hes66b], with corrections.

Hestenes:1980:CDM

[Hes80c] Magnus R. Hestenes. Conjugate Direction Methods in Optimization, volume 12 of Applications of Mathematics. Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 1980. ISBN 0-387-90455-7 (New York), 3-540-90455-7 (Berlin). ISSN 0172-4568. x + 325 pp.

Hestenes:1983:SQV

[Hes83]  M. R. Hestenes.  Singular

quadratic variational problems. Journal of Optimization Theory and Applications, 41(1):123– 137, September 1983. CO-DEN JOTABN. ISSN 0022-3239 (print), 1573-2878 (electronic).

Hestenes:1987:CGV

[Hes87] M. R. Hestenes. Conjugacy and gradients in variational theory and analysis. In Crane [Cra87], pages 71–90. ISBN 0-89791-229-2. LCCN QA76 .A25 1987.

Hestenes:1990:CG

[Hes90] Magnus R. Hestenes. Conjugacy and gradients. In Nash [Nas90], pages 167–179. ISBN 0-201-50814-1. LCCN QA76.17 .H59 1990.

Hestenes:2013:ECV

[Hes13] Magnus R. Hestenes. Elements of the calculus of variations. In Beckenbach [Bec13a], chapter 4, page ?? ISBN 0-486-49746-1 (paperback), 0-486-31611-4 (ebook). LCCN QA401 .B4 2013. With an introduction by Royal Weller. Reprint of [Bec56].

Hestenes:1968:ETD

[HG68] M. R. Hestenes and T. Guinn. An embedding theorem for differential equations. Journal of Optimization Theory and Applications, 2(2):87–101, March 1968. CODEN JOTABN. ISSN 0022-3239 (print), 1573-2878 (electronic).

Hestenes:1951:S

[HK51a] M. R. Hestenes and W. Karush. Solutions of Ax = λBx. Journal of Research of the National Bureau of Standards (1934), 47(6): 471–478, December 1951. ISSN 0091-0635. Research paper 2275.

Hestenes:1951:MGC

[HK51b] Magnus R. Hestenes and William Karush. A method of gradients for the calculation of the characteristic roots and vectors of a real symmetric matrix. Journal of Research of the National Bureau of Standards (1934), 47(1): 45–61, July 1951. ISSN 0091-0635.

HassanIbrahim:2022:DFT

[HKH^{+}22] Abdulkarim Hassan Ibrahim, Poom Kumam, Basim A. Hassan, Auwal Bala Abubakar, and Jamilu Abubakar. A derivativefree three-term Hestenes–Stiefel type method for constrained nonlinear equations and image restoration. International Journal of Computer Mathematics, 99 (5):1041–1065, July 2022. CO-DEN IJCMAT. ISSN 0020-7160.

Hestenes:1940:TQF

[HM40] M. R. Hestenes and E. J. Mc-Shane. A theorem on quadratic forms and its application in the calculus of variations. Transactions of the American Mathematical Society, 47(3):501–512, May 1940. CODEN TAMTAM. ISSN 0002-9947 (print), 1088-6850 (electronic).

Hestenes:1939:NWC

[HR39] M. R. Hestenes and W. T. Reid.

A note on the Weierstrass condition in the calculus of variations. Bulletin of the American Mathematical Society, 45(6):471–473, June 1939. CODEN BAMOAD. ISSN 0002-9904 (print), 1936-881x (electronic).

Hestenes:1974:MCQa

[HR74a] Magnus Hestenes and Ray Redheffer. On the minimization of certain quadratic functionals. I. Archive for Rational Mechanics and Analysis, 56(1):1– 14, March 1974. CODEN AVR-MAW. ISSN 0003-9527 (print), 1432-0673 (electronic).

Hestenes:1974:MCQb

[HR74b] Magnus Hestenes and Ray Redheffer. On the minimization of certain quadratic functionals. II. Archive for Rational Mechanics and Analysis, 56(1):15– 33, March 1974. CODEN AVR-MAW. ISSN 0003-9527 (print), 1432-0673 (electronic).

Hestenes:1951:SLE

[HS51] Magnus R. Hestenes and Marvin L. Stein. The solution of linear equations by minimization. NAML Report 52-45, National Bureau of Standards, Los Angeles, CA, USA, December 12, 1951.

Hestenes:1952:MCG

[HS52] Magnus R. Hestenes and Eduard Stiefel. Methods of conjugate gradients for solving linear systems. Journal of Research of the National Bureau of Standards (1934), 49(6):409–436, December 1952. ISSN 0091-0635 (print), 2376-5305 (electronic). Research paper 2379.

Hestenes:1973:SLE

[HS73] M. R. Hestenes and M. L. Stein. The solution of linear equations by minimization. Journal of Optimization Theory and Applications, 11(4):335–359, April 1973. CODEN JOTABN. ISSN 0022-3239 (print), 1573-2878 (electronic).

Hestenes:1991:NIN

[HT91] Magnus R. Hestenes and John Todd. NBS-INA, the Institute for Numerical Analysis, UCLA 1947–1954. National Technical Information Service, Washington, DC, USA, August 1991. x + 198 (various) pp. URL https:/

/nvlpubs.nist.gov/nistpubs/
Legacy/SP/nistspecialpublication730.

pdf. Cover title: Mathematicians learning to use computers: the Institute for Numerical Analysis, UCLA, 1947–1954. Spine title: The Institute for Numerical Analysis, UCLA, 1947–1954. Sponsored in part by the Mathematical Association of America. Shipping list no.: 92-1306-M.

Hu:2020:SMH

[HWY20] Wujie Hu, Jinzhao Wu, and Gonglin Yuan. Some modified Hestenes–Stiefel conjugate gradient algorithms with application in image restoration. Applied Numerical Mathematics: Transactions of IMACS, 158(??): 360–376, December 2020. CO-DEN ANMAEL. ISSN 0168-9274 (print), 1873-5460 (elec-

tronic).  URL http://www.
sciencedirect.com/science/
article/pii/S0168927420302440.

Japri:2021:NMH

[JBM21] Nur Athira Japri, Srimazzura Basri, and Mustafa Mamat. New modification of the Hestenes– Stiefel with strong Wolfe line search. In AIP Conference Proceedings: SCIEMATHIC 2020, volume 2355. American Institute of Physics, Woodbury, NY, USA, 2021.

Jeroslow:1977:BRO

[Jer77] Robert G. Jeroslow. Book review: Optimization theory, the finite dimensional case, by Magnus R. Hestenes, John Wiley and Sons, New York, London, Sydney, Toronto, 1975, xiii + 447. Bulletin of the American Mathematical Society, 83(3):324–336, May 1977. CODEN BAMOAD. ISSN 0002-9904 (print), 1936-881X (electronic).

Jittorntrum:1980:ACP

[Jit80] Krisorn Jittorntrum. Accelerated convergence for the Powell– Hestenes multiplier method. Mathematical Programming, 18 (2):197–214, December 1980. CODEN MHPGA4. ISSN 0025-5610 (print), 1436-4646 (electronic).

Khoshsimaye-Bargard:2023:DFS

[KBA23a] Maryam Khoshsimaye-Bargard and Ali Ashrafi. A descent family of the spectral Hestenes– Stiefel method by considering the quasi-Newton method. Optimization Methods and Software, 38(3):495–509, January 2023. ISSN 1026-7670 (print), 1055-6788 (electronic).

Khoshsimaye-Bargard:2023:FMT

[KBA23b] Maryam Khoshsimaye-Bargard and Ali Ashrafi. A family of the modified three-term Hestenes–Stiefel conjugate gradient method with sufficient descent and conjugacy conditions. Journal of Applied Mathematics and Computing, 69(3):2331– 2360, January 2023. ISSN 1598-5865 (print), 1865-2085 (electronic).

Lee:1995:CPM

[Lee95] J. A. N. Lee. Computer pioneers: Magnus R. Hestenes. IEEE Web site., 1995. URL https://

history.computer.org/pioneers/
hestenes.html.

Landesman:1991:LAA

[LH91] Edward M. Landesman and Magnus Rudolph Hestenes. Linear Algebra: With Applications for Mathematics, Science, and Engineering. Prentice-Hall, Upper Saddle River, NJ 07458, USA, 1991. ISBN 0-13-529561-0 (hardcover), 0-13-534967-2 (paperback). LCCN QA184 .L364 1991.

Lide:2001:CEM

[Lid01] D. R. Lide, editor. A Century of Excellence in Measurements, Standards, and Technology: A Chronicle of Selected NBS/NIST Publications, 1901– 2000, volume 958. National Technical Information Service, Washington, DC, USA, 2001. ix + 386 pp. URL https:/

/nvlpubs.nist.gov/nistpubs/
sp958-lide/cntsp958old.htm.

NIST Special Publication.

Li:2022:MTT

[LLW22] Dandan Li, Yuangfei Li, and Songhua Wang. A modified three terms Hestenes–Stiefel conjugate gradient projection algorithm and its application. Journal of Jilin University. Science Edition. Jilin Daxue Xuebao. Lixue Ban, 60(1):64–72, 2022. ISSN 1671-5489.

Maehly:1954:IAA

[Mae54]  Hans J. Maehly.  Zur iter-

ativen Auflösung algebraischer Gleichungen. (German) [On the iterative solution of algebraic equations]. Zeitschrift für Angewandte Mathematik und Physik = Journal of Applied Mathematics and Physics, 5(3):260–263, May 1954. CODEN ZAMPDB. ISSN 0044-2275 (print), 1420-9039 (electronic).

Miele:1974:APM

[Mie74] A. Miele. An appreciation of Professor M. R. Hestenes. Journal of Optimization Theory and Applications, 14(5):445–451, November 1974. CODEN JOTABN. ISSN 0022-3239 (print), 1573-2878 (electronic). Includes a list of 58 publications of Magnus Hestenes.

Nash:1990:HSC

[Nas90] Stephen G. Nash, editor. A History of Scientific Computing. ACM Press history series. Addison-Wesley and ACM Press, Addison-Wesley and New York, NY 10036, USA, 1990. ISBN 0-201-50814-1. xix + 359 pp. LCCN QA76.17 .H59 1990.

Narayanan:2021:LHD

[NK21] Sindhu Narayanan and P. Kaelo. A linear hybridization of Dai– Yuan and Hestenes–Stiefel conjugate gradient method for unconstrained optimization. Numerical Mathematics. Theory, Methods and Applications, 14(2):527– 539, June 2021. ISSN 1004-8979 (print), 2079-7338 (electronic).

OLeary:2001:IMS

[O’L01a] Dianne P. O’Leary. Iteration method for the solution of the eigenvalue problem of linear differential and integral operators. In Lide [Lid01], pages 77–80. URL https:/

/nvlpubs.nist.gov/nistpubs/
sp958-lide/077-080.pdf. NIST

Special Publication.

OLeary:2001:MCG

[O’L01b] Dianne P. O’Leary. Methods of conjugate gradients for solving linear systems. In Lide [Lid01], pages 81–85. URL https:/

/nvlpubs.nist.gov/nistpubs/
sp958-lide/077-080.pdf. NIST

Special Publication.

Pellegrini:1991:EHN

[Pel91] L. Pellegrini. An extension of the Hestenes necessary condition. Journal of Optimization Theory and Applications, 69(2):297–309, May 1991. CODEN JOTABN. ISSN 0022-3239 (print), 1573-2878 (electronic).

Profera:1977:SAH

[Pro77] Luigi Profera. Simple Artinian Hestenes ternary rings. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8), 62(3):292– 299, 1977. ISSN 0392-7881.

Paige:1953:SLE

[PT53] L. J. (Lowell J.) Paige and Olga Taussky, editors. Simultaneous Linear Equations and the Determination of Eigenvalues[: proceedings of a symposium held 23– 25 August 1951 at the Institute for Numerical Analysis, Los Angeles, California], volume 29 of Applied Mathematics Series. U.S.

National Bureau of Standards, Gaithersburg, MD, USA, 1953. LCCN QA3 .U5 no. 29.

Qi:1996:MHS

[QHL96] Hou Duo Qi, Ji Ye Han, and Guang Hui Liu. The modified Hestenes–Stiefel conjugate gradient method. Chinese Annals of Mathematics. Series A. Shuxue Niankan. A Ji, 17(3):277–284, 1996. ISSN 1000-8314.

Raihen:2017:CRH

[Rai17]  Nurul Md Raihen.  Con-

vergence rates for Hestenes’ Gram–Schmidt conjugate direction method without derivatives in numerical optimization. Master’s thesis, University of Toledo, Toledo, OH, USA, August 2017. x + 37 pp.

                                        URL https://www.proquest.
                                        com/pqdtglobal/docview/2166237834.

Reid:1971:LSS

[Rei71a] John Ker Reid, editor. Large Sparse Sets of Linear Equations: Proceedings of the Oxford Conference of the Institute of Mathematics and its Applications held at St. Catherine’s College, Oxford, 5–8 April 1970. Academic Press, New York, USA, 1971. ISBN 0-12-586150-8 (hardcover). x + 284 pp. LCCN QA195 .L37 1971.

Reid:1971:MCG

[Rei71b] John Ker Reid. On the method of conjugate gradients for the solution of large sparse systems of linear equation. In Large Sparse Sets of Linear Equations: Proceedings of the Oxford Conference of the Institute of Mathematics and its Applications held at St. Catherine’s College, Oxford, 5–8 April 1970 [Rei71a], pages 231– 254. ISBN 0-12-586150-8 (hardcover). LCCN QA195 .L37 1971.

Rosser:1951:SCE

[RLHK51] J. B. Rosser, C. Lanczos, M. R.

Hestenes, and W. Karush. Separation of close eigenvalues of a real symmetric matrix. Journal of Research of the National Bureau of Standards (1934), 47(4): 291–297, October 1951. ISSN 0091-0635 (print), 2376-5305 (electronic). Research Paper 2256.

Rivaie:2010:MHS

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