A Bibliography of Publications of William M. Kahan

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: [email protected], [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 12 March 2021 Version 1.71

Title word cross-reference 2-Dimensional [166]. 2007 [328]. 25th [323]. 2nd [236].

50th [328]. 52 [52]. 55 [195]. 128 [276]. 2 [216, 263]. 2 × 2 [306]. 3 60 [31, 35]. 6600 [41]. 6600/7600 [41]. [216, 263]. A4 [266]. A4z = b [266]. f(x)=0 [57]. ∞/∞ [284]. M [67]. n × n [42]. p ≥ 0 7094 [18, 22]. 7094-II [18, 22]. 754 [206]. QR√ [32]. q × m − n [73]. → [248]. sin Θ [151]. x [63]. x ∗ [1/x] < x/x = 1 [128]. xn [133, 140, 309, 174]. 754r [288]. 75th [328]. [177]. Z [42, 179, 269]. 7600 [41]. 7th [321]. z =(1− exp(−pz))/(pz) [206]. z ≥ 0 [206]. k − ∗k≤k ∗k 8087 [74]. ’83 [320]. Z Z Z + Z (log2 n +0.038) [42].

-Dimensional [216, 263]. -matrices [67]. Abbreviated [244]. Abstract [15]. -plane [179, 269]. Abstracts [265]. Accuracy [93, 99, 106, 127, 296, 105, 150]. Accurate 1 [152]. 128B [277, 278]. 12th [316, 329]. [102, 233, 213, 14, 290, 306]. Accurately 14th [324]. 15C [74]. 167 [4]. 168 [6]. 169 [308]. ACM [325, 313, 176]. ACM/IEEE [5]. 1971 [40]. 1975 [315, 314]. 1983 [320]. [325]. ACRITH [80]. Addition [13]. Adds 1986 [322]. 1999 [196]. [112]. Adjugate [245]. Ado [88].

1 2

Advantages [126]. Aitken [60]. Alan [176]. Boats [235]. Boston [313]. Boulder [318]. Algebra [101, 233, 17, 107, 222, 87]. Bound [15, 21, 67]. Bounds algebraic [310]. ALGOL [35, 31, 35, 31]. [68, 282, 29, 71, 244, 297, 30, 28, 287, 20]. Br Algorithm [304, 184, 217, 77, 261, 310, 306, [317]. Branch [69, 88]. Brand [236]. Brief 124, 32, 4, 5, 6]. Algorithms [43, 44, 45]. [283]. Bus [210]. Business [285]. Almost [34, 94, 138]. Almost-Commuting [34]. American [319]. Anadromic [294]. Calculating [9, 97]. Calculation [4]. Analyses [139, 160]. Analysis Calculations [244]. Calculator [152, 322, 18, 22, 37, 45, 111, 116, 122, 77, [51, 57, 61, 55]. California [325, 320, 180]. 324, 306, 301, 27]. Analyst [254]. Can [233, 51, 55, 142, 292]. Canada Angewandte [317]. Angle [97, 234, 267]. [319, 316]. can’t [292]. Cantilever [148]. Angles [147, 223]. anniversary [328]. cases [133]. Cayley [279, 289]. CDC [41]. Annual [313, 319, 316]. Anomalies [80]. celebrating [328]. Center [327]. certain Answers [153, 214]. Any [57, 238]. [133]. certification [290]. Challenges [107]. aphorisms [26]. Application [122]. Chapter [43]. \ [270]. Checking [89, 113]. Applications [68, 305, 288, 149]. Applied Chemistry [145, 136]. Chió [154]. Circle [145, 307, 136]. Approach [213]. [24]. Circumscribing [25]. class [149]. Approximate [71, 234]. Approximation Classification [246]. Clean [100]. Cleve [164]. Approximations [199]. Apr. [40]. [309]. Clever [274]. Clouds [257]. April [322]. Area [97, 147, 223]. Argonne Clustered [134]. Clusters [23]. [315]. Arithmetic Coefficients [154, 209]. Coins [178]. [78, 79, 56, 298, 321, 27, 29, 62, 66, 82, 83, Colorado [318]. Combinatorial [209]. 90, 98, 100, 110, 131, 229, 239, 255, 268, 285, Commentary [29, 299]. Commutators 48, 64, 329, 309, 30, 72, 103, 104, 133, 140, [197]. Commuting [34]. Compensated 142, 224, 230, 58, 75, 76, 146]. Arithmetics [122]. Complete [27]. completely [52]. [213]. Arithmetik [48, 64]. arrival [328]. Complex [69, 88, 110, 120, 179, 269]. Art [328, 322]. Assessments [271]. Complexity [233, 181]. Composition [144]. Assignment [266]. assistant [295]. Computable [15]. Computation [304, 233, Association [319]. Augmenting [110]. 138, 200, 268, 271, 293, 318, 306, 104]. August [313, 319, 312, 318]. Award Computational [328, 106]. Computations [176, 264]. Axioms [167, 215]. [315, 139, 160]. computed [81]. Computer [316, 321, 29, 94, 127, 145, 240, 254, 329, 30, Babuska [31, 35]. Babuska’sche [31, 35]. 136]. Computer-Arithmetic [30]. Back [293]. Backward [6, 311]. Baleful Computerized [107]. Computers [145, 136]. Bases [172]. be [91, 104, 123]. [101, 41, 1, 124]. Computing Beastly [137]. Before [309]. Benchmarks [325, 326, 327, 212, 93, 233, 328, 308, 117, [127, 145, 136]. Beresford [303]. Besieged 177, 245, 329, 319, 242, 299]. Concepts [285]. Bessel [20]. Better [103]. Between [99, 106, 105]. Concerning [29, 26]. [318, 117]. Bidiagonal [93, 102]. Bilinear Condition [39]. Conference [164]. Binary [313, 325, 324, 322, 318, 328, 320, 329]. [56, 58, 82, 95, 131, 146, 248, 114, 140]. Confirming [113]. Confluence [39]. Birmingham [322]. birthday [328]. Bit Confluent [4]. Congress [312]. Conic [88]. Blabber [235]. Blabber-Mouth [235]. [179]. Conjugate [266, 272]. Conserving blame [301]. BLAS [232, 260]. block [310]. [39]. Constant [135]. Constant-Round 3

[135]. constants [144]. Construct [135]. Down [125]. Draft [56]. Dual [172]. Contains [24]. continuation [218]. Duisburg [329]. Dundee [324]. Continued [92]. Contracted [112]. Contribution [65]. Convention [327]. Echelon [168]. Editorial [303]. Effect convergence [67, 32]. Conversation [150]. [145, 136]. efficiently [212, 242]. Conversion [248, 114]. Corner [309]. Eigenproblem [123]. Eigensystems Correct [304]. Correcting [113]. [71, 256]. Eigenvalues [134, 14, 23]. correction [124]. Correctly [95, 141, 89]. Eigenvectors [3, 8, 33]. electronic [1]. Cost [181, 268]. Count [51, 55]. Course Elementary [69, 88, 156, 218]. elements [27]. Covered [231]. Cray [323, 104]. CRC [19]. Elicited [173]. ellipse [46]. ellipsoid [299]. Cross [216, 263]. Cross-Products [25]. Ellipsoidal [244, 21]. ellipsoids [25]. [216, 263]. CS [58]. Cubic [85]. Curbs [39]. End [299]. Engineering [293, 27]. Curmudgeon [254]. Cuts [69, 88]. Enumerating [189]. Environment [65]. Environments [70]. Equation D. [44]. Dallas [327]. Dates [117]. [57, 85, 255, 280, 1, 149, 206]. Equations Davidson [308]. Davis [86, 151]. [15, 154, 310, 2, 21, 144, 149, 294]. Error Davis-Kahan [151]. [68, 282, 287, 15, 29, 37, 139, 160, 244, 280, Davis-Kahan-Weinberger [86]. Day [117]. 297, 299, 30, 41, 21, 124, 311]. Error-Bound DAYDATE [117]. Days [117]. Debate [15]. Error-Bounds [297]. Errors [11]. etc [298]. debug [292]. Dec [40]. Decimal [74, 117]. Euclid [184, 217]. Euclidean [82, 248, 114]. Decisions [285]. Dedicated [216, 263]. Evaluates [61]. Evaluation [84]. [303]. Deficient [247]. Defined [91]. ever [266]. Every [42]. Everyone Definition [48, 64]. Degrades [148]. [158, 159]. Everywhere [158, 159]. exact Demonstration [284]. Derangements [87]. Exam [182]. Derivative [161]. Derivatives [185, 186, 187, 188, 190, 201, 231, 249]. [259, 269]. describe [103]. Design Examination [153, 214]. Exception [118]. [229, 232, 260, 26, 224, 230]. Designers [72]. Exception-Handling [118]. Extended Designing [108, 109, 115]. Determinant [232, 310, 260]. Extension [161]. Determinants [125, 306]. [101, 152, 143, 175]. Extra [282, 268, 287]. Developers [286]. Diagnostics [70]. Extra-Precise [268, 287]. Extrapolation Diagonal [14, 155, 279, 19, 289]. [60, 251]. eye [267]. Differences [4, 5, 6, 200, 259]. different [52]. Differential Factorizations [258]. Failure [270]. family [15, 255, 280, 310, 21, 144, 149, 294]. [294]. far [49, 54]. Fclass [246]. Federation difficult [133]. digit [238]. Digital [72]. [312]. Fermat [192]. Few [308]. Fields dilation [86]. Dilations [68]. Dilemma [215]. Final [153, 190, 201, 214, 249]. [302]. Dimensional [166, 216, 263]. Finders [296]. Finding [162, 163, 273]. Directions [328]. discrete [307]. Floating Discriminant [304, 290]. Discussion [78, 79, 56, 152, 233, 10, 59, 58, 62, 63, 66, [183, 32]. Divided [4, 5, 6, 200]. divider 75, 76, 82, 83, 90, 95, 118, 131, 146, 158, 159, [238]. Division [132, 205, 89]. Do 229, 237, 239, 246, 268, 271, 285, 293, 309, 13, [66, 239, 270, 233, 240]. done [104]. Double 301, 173, 26, 89, 133, 140, 142, 224, 230, 295]. [12, 13]. Double-Precision [12, 13]. Floating-Point [78, 10, 59, 63, 66, 75, 76, Doubled [90]. Doubled-Precision [90]. 82, 83, 90, 95, 118, 131, 146, 158, 159, 229, 4

237, 239, 246, 268, 271, 285, 293, 173, 79, [38, 39, 50, 307]. Ill-Condition [39]. 301, 89, 133, 140, 142, 224, 230, 295]. Form Ill-Posed [38, 50, 307]. Illinois [321]. IMA [168, 220, 221]. Formally [304]. Formats [322]. IMA/SIAM [322]. IMACS [329]. [237]. Forms [164]. Formula [161]. Implementation [43, 44, 48, 232, 64, 260]. Forsythe [328]. FORTRAN [7, 16, 238]. Implementierung [64, 48]. important Forward [5]. Four [26]. FPTRP [10]. [150]. Improbability [139, 160, 191]. Fractions [92]. Fragility [191]. Francisco Improvement [77]. Improving [87]. [320]. Freiburg [317]. function [206]. Inclusion [23]. independent [78, 79]. Functions [69, 88, 20, 81]. Further Inequalities [202]. Inequality [225]. [306, 143, 175, 11]. Futile [271]. Futility Infinitely [236]. Infinity [243]. [98]. Future [328, 293]. Information [312]. Institut [317]. Instruments [52]. Integer [154]. Integers Gain [165]. GAMM [329]. [189]. Integrals [61, 87]. integrator [129]. GAMM-IMACS [329]. Gauss [2, 157]. Intel [74]. interface [316]. International Gaussian [60]. GCD [184, 217]. Gene [312, 329, 317, 314]. Interpolation [328]. Genealogy [281]. Generalization [5, 6, 251]. intersection [25]. Interval [143, 175]. Generalized [247]. generating [27, 62, 255, 317, 314]. Interval-Arithmetic [20]. Geometry [156, 218]. George [328]. [255]. Interview [173, 174]. Introduction German [55, 48, 64, 31, 35]. Germany [72]. inv [270]. invariant [311]. Inverse [314, 317, 329]. Get [38]. Givens [212, 242]. [9, 123]. Inverses [247, 250, 258]. Inversion globally [311]. go [49, 54]. Golub [157]. Invited [29]. Irrationals [199]. [328, 310, 307, 308]. Good [75, 76]. got irreducible [67]. Iterate [272]. Iteration [235]. Grades [219]. Gradient [266]. [119, 266]. Iterative [282, 287]. IV [16]. Gradients [272]. Gradual [283]. Great [298]. Group [323]. Gu [275]. Guaranteed Jacobi [161]. Java [326, 152, 158, 159]. [93]. Gustafson [299, 298]. Jensen [225]. Jiang [311]. John [299, 298, 145]. Joint [322]. Jordan H. [204]. H110 [216, 219]. H90 [225]. Half [157, 221]. Jose [325]. June [323, 324, 321]. [274]. Halting [193]. Handheld [61]. Handling [118]. hardware [26]. K. [29]. Kahan Haugeland [44]. held [322, 317]. Help [38]. [308, 48, 64, 86, 31, 35, 264, 175, 176, 281, 310, Hermitian [23, 47]. High 304, 303, 134, 307, 298, 306, 53, 48, 64, 67, [325, 326, 327, 101, 93, 108, 109, 115]. 31, 35, 77, 129, 173, 174, 311, 150, 151, 143]. High-Performance [326, 101]. Higher [98]. Kahan-Arithmetik [48, 64]. Higher-Precision [98]. Hilbert [250]. Kahan-Babuska [31, 35]. Hirondo [40]. Home [170, 277]. Hough Kahan-Babuska’sche [31, 35]. Karlsruhe [44]. hour [142]. HP [74]. HP-15C [74]. [314]. Keplerian [300]. Key [57]. Huge [247]. Hurts [158, 159, 104]. Knowledge [135]. Können [55]. Korteweg [149]. Kuki [40]. IBM [80]. Idealized [148]. Idempotent [248]. IEEE [325, 58, 62, 63, 75, 76, 90, 131, L [299]. Laboratory [315]. Laguerre 133, 140, 146, 288, 309, 114, 174]. IEEE-CS [24, 119]. Lanczos [307, 45, 49, 54]. [58]. IFIP [312, 318]. Ihre [48, 64]. Ihren Language [110]. Languages [145, 240, 318]. [55]. II [8, 18, 22, 235]. III [33]. Ill LAPACK [101, 291]. Large 5

[308, 194, 310, 2]. Last [304]. Law [194]. [29]. No [94, 138, 53]. Nobody [165]. LCAS [111, 116]. learn [142]. Least Nonnormal [71]. nonsingular [67]. Norm [24, 164]. Least-Squares [164]. Lecture [68, 86]. Norm-Preserving [68, 86]. [27, 44, 131, 140, 145, 146, 162, 163, 244, 273]. Normal [221]. Norms [226, 211, 241]. Note length [78, 79]. Lenstra [204]. Libraries [20, 12, 175, 151]. Notes [108, 109, 115, 291]. Library [101]. Like [27, 44, 119, 131, 146, 162, 166, 204, 216, 225, [97, 147, 223]. Linear 226, 244, 273, 140, 218]. Nothing [88]. [101, 233, 17, 154, 222, 2, 21]. Little [192]. November [325, 327, 320]. NP [135]. Ljubljana [312]. Local [280]. Logarithm Numbers [121, 137, 194]. Numerical [274]. logic [238]. Loss [165]. Lotfi [130]. [108, 109, 115, 233, 328, 324, 322, 18, 17, 22, Lottery [180]. lu [270]. 27, 70, 113, 139, 160, 254, 286, 318, 294, 150]. Numerically [100]. Numerics [329]. M [176]. M. [236]. Man [173]. Many [236]. March [328]. Marketing [224, 230]. Math Occasional [98]. ODE [262]. off [19]. [216, 249, 277, 278, 195, 196]. Math. off-diagonal [19]. Old [173]. One [24, 142]. [219, 225]. Mathematics Only [197]. Ontario [323, 316]. Open [286]. [328, 74, 145, 224, 230, 136, 314, 317, 281]. Operands [246]. Operations [156, 218]. Mathematik [317]. MATLAB Optimal [68, 311]. Options [62]. Orbits [270, 165, 250, 251, 262]. Matrices [300]. orders [144]. Ordinary [93, 102, 308, 305, 23, 34, 45, 71, 247, 250, [15, 255, 21, 144, 149]. organized [312]. 258, 211, 241, 19, 47, 67]. Matrix [315, 9, Orthogonality [70]. other [224, 230]. Our 14, 42, 157, 222, 143, 175, 310, 266, 294]. [106, 167]. Over/Underflow [10]. Max [91]. May [314, 317, 316]. Meeting Overrelaxation [272]. [323, 319]. memoriam [40]. Method [308, 24, 31, 35]. methods [307, 1, 2, 294]. p754 [75, 76]. Package [80]. Pairs [189]. Michigan [27]. Micro [320, 320]. Paper [29]. papers [319]. Paradoxes MidTerm [252, 253]. might [104]. Min [99, 105, 106]. parallel [124]. Parlett [91]. Mindless [271]. Ming [275]. Mini [311, 303]. Part [130]. Performance [320, 320]. Mini/Micro [320, 320]. [325, 326, 327, 101, 108, 109, 115]. Personal Minimizing [73]. Miscalculating [57]. Perturbation [3, 8, 33, 28, 311]. [147, 223]. Mixed [232, 260]. Mode [270]. Physics [145, 136]. Pinchings [211, 241]. Model [185, 186, 187, 188, 190, 208]. Pitfalls [50]. Plane [257, 179, 269]. Modes [288]. Moments [305]. Platforms [213]. Point monotonicity [81]. Mortem [7]. Morton [78, 56, 152, 233, 10, 59, 58, 62, 63, 66, 75, 76, [281]. Mouth [235]. Much [88]. 82, 83, 90, 95, 118, 131, 146, 158, 159, 229, Multiplication [95, 120]. Multiply [112]. 237, 239, 246, 268, 271, 285, 293, 309, 13, 173, Multiply-Adds [112]. Must [258]. 79, 26, 89, 133, 140, 142, 224, 230, 295, 301]. Poisson [1]. Polynomial Names [237]. National [315]. Near [34, 70]. [233, 24, 84, 296, 297]. Portable nearly [47]. Need [66, 239]. Needle [101, 108, 109, 115, 123]. Posed [38, 50, 307]. [97, 147, 223]. Needle-Like [97, 147, 223]. Post [7, 329]. Post-Mortem [7]. neglect [19]. neighboring [267]. Network post-proceedings [329]. Pracniques [11]. [326]. Networking [325, 327]. Neumann practical [32]. Precimonious [295]. [145]. Newton [5, 6]. Next [291]. Nickel Precise [282, 268, 287]. Precision 6

[90, 98, 232, 12, 13, 260, 295, 301]. [3, 8, 33]. Rotations [216, 263, 212, 242]. prescribe [103]. presented [319, 320]. Round [135]. Rounded [95, 141, 89]. Preserving [68, 86]. Press [299]. Rounding [288]. Roundoff Presubstitution [92, 284]. Probabilistic [41, 84, 120, 148, 271]. Routine [10]. Row [139, 160]. Probability [96]. Problem [168]. Row-Echelon [168]. Ruminations [38, 36, 167, 169, 193, 198, 227, 228, 236, 46, [224, 229, 230]. 53, 86]. Problems [50, 167, 171, 203, 204, 209, 258, 278, 307, 183]. S [44]. S.O.R. [67]. San [325, 320]. Sand Procedure [7]. Proceedings [74]. Satisfies [42]. SC2000 [327]. SC97 [313, 325, 315, 323, 316, 321, 322, 318, 319, [325, 325]. ScaLAPACK [291]. scaled 312, 324, 329, 314, 317]. process [49, 54]. [211, 241]. SCAN [329]. schemes [144, 149]. processing [312]. Products [216, 263]. Science [254, 293, 316]. Scientific Prof. [275]. Program [329, 104]. section [319]. Sections [179]. [65, 94, 256, 114, 238]. Programmer [123]. Seidel [2]. selection [238]. Semantics Programming [65, 70, 110, 240, 318]. [152, 70]. Semiannual [323]. Separation programs [133, 251, 292]. Project [281]. [257]. September [315, 329]. Series [280]. Prominence [155]. Proof [290, 135]. sessions [320]. Set [167, 169]. Sharp [134]. Proposal [152]. Proposed Should [91, 49, 54]. SIAM [322]. sich [55]. [78, 79, 56, 59, 58, 62, 63, 75, 76, 246]. sided [311]. Sign [88]. Significance Prospectus [101, 291]. Proven [304]. [94, 138]. SIGSAM [53]. Simply [122]. Pseudo [9]. Pseudo-Inverse [9]. Purposes Singular [93, 102, 308, 9]. Singularity [231]. [100]. Skew [279, 289]. Small [93, 289]. Software [63, 113, 286]. solution [53, 86]. QDRTC [16]. QR [261]. Quadratic [220]. Solutions [169, 170, 171, 185, 186, 187, 188, Quadrature [305, 60]. Quasi [12, 13]. 190, 198, 201, 203, 204, 208, 227, 228, 236]. Question [286]. quotient [238]. Solve [57, 85, 206, 266]. Solver [280]. quotient-digit [238]. SOLVEzag [206]. solving [1, 2]. Some [28, 202, 81, 292]. something [52]. Space Radix [78, 79]. Radix- [78, 79]. raising [167]. Spaces [166, 172, 215, 216, 263]. [144]. Rank [247]. Rank-Deficient [247]. Sparse [315, 308, 315]. Spectra [47]. Rational [83, 199]. Real Spectrum [42]. Spring [196]. SQRT [141]. [42, 85, 162, 163, 273]. Rechner [55]. Square [205, 276]. Squares [164, 276]. SR Reciprocal [259]. Recognize [220]. record [52]. SR-52 [52]. SRT [132, 238]. SRTEST [320]. recurrence [20]. Reduced [168]. [238]. Stack [126]. Stamps [178]. Standard Reducing [11]. reduction [307]. Refine [78, 79, 56, 59, 58, 63, 66, 75, 76, 90, 140, [256]. Refineig [256]. Refinement 146, 239, 246, 62, 131]. Standardized [237]. [282, 287]. Refutation [111, 116]. Standards [174]. Stanford [328, 328]. Relationship [318]. Relative [93]. reliably stars [267]. State [328, 322]. statistical [212, 242]. Remarks [11]. Reminiscences [319]. statistics [316]. Status [173]. Removable [100]. Residual [71]. [131, 146, 140]. storing [266]. Study Revised [236]. Revision [152]. Riccati [143, 175]. subroutine [16]. Subspaces [310, 294]. Robustness [65]. Root [218, 28, 311]. subtended [267]. suitable [162, 163, 205, 273]. Root-Finding [1]. Suite [262, 133]. Summation [162, 163, 273]. Roots [276]. Rotation [122, 31, 77, 35, 124]. Summer [27]. REFERENCES 7

Summierungsverfahren [31, 35]. Sunk ing/Testing/Confirming/Checking/Correcting [235]. Super [180]. Support [18, 22]. [113]. Values [93, 102, 9]. Vector Survey [37, 1]. Syllabus [195, 196]. [167, 172, 215, 226]. verlassen [55]. Version Symbolic [233, 107, 200, 87]. Symmetric [134]. Versus [82, 127, 224, 230]. Visions [14, 45, 19]. symplectic [129]. Symposium [130]. Volume [240]. Vries [149]. vs [315, 321, 329, 317, 316, 314]. Syntax [70]. [298, 181]. System [18, 22]. Systems [135, 15, 107, 72, 87, 2, 21]. W [204]. W. [44, 129]. Waiting [210]. War [235]. Waterloo [316]. Week [117]. Take [170, 277]. Take-Home [170, 277]. Weinberger [86]. Well [38]. West tanpi [302]. Taylor [280]. TC2 [318]. Test [320, 314]. West-83 [320]. Whether [95, 132, 141, 170, 171, 207, 208, 252, 253, [95, 89]. Which [24]. William 277, 238]. Testing [113, 232, 114, 133, 260]. [176, 281, 303, 298, 264, 173, 174, 150]. Tests [296]. Tetrahedron [240]. Texas [52]. Winner [264]. Without [205, 268, 266]. text [183]. their [68]. Theorem Word [78, 79]. Word-length-independent [134, 192, 143, 175, 311, 151]. Theorems [78, 79]. Working [318]. Workshop [326]. [23]. Theory [222, 96]. there [279, 289]. World [235]. Would [123]. Would-be Thiele [259]. Three [209, 278]. Time [233]. [123]. Written [74]. titled [218]. Too [274]. Topics [231]. Toronto [319, 323]. Trace [197]. Yugoslavia [312]. Trajectory [244]. Transcription [298]. Transform [279, 289]. Transparencies Zero [135, 24, 197, 279, 296, 297, 289]. Zero- [275]. Trap [10]. Travails [123]. Tri [14, 19]. Finders [296]. Zero-Knowledge [135]. Tri-Diagonal [14, 19]. Triangle [97, 147, 223]. Triangular [258, 211, 241]. Trick [154]. Tridiagonal [123]. Tripleo References [64]. Triplets [308]. Triplex [31, 35, 31, 35]. Kahan:1955:SMS Triplex-ALGOL [35, 31, 35, 31]. Trisection [234]. Truncation [11]. Tuning [1] William Morton Kahan. A survey of [295, 301]. Turing [176, 264]. Tutorial [283]. methods of solving Poisson’s equation Twenty [107]. Two [258, 25, 183, 311]. suitable for electronic computers. M.A., two-sided [311]. TX [327]. University of Toronto, Toronto, ON, Canada, 1955. ii + 44 + 8 pp. U [235]. U-Boats [235]. UCBTEST [133]. Unconventional [149, 144, 129]. Kahan:1958:GSM Undebuggable [293]. Underflow [10, 283]. Unique [168, 258]. Universität [317]. [2] William Morton Kahan. Gauss–Seidel University [328, 316, 321, 322, 27]. Unum methods of solving large systems of lin- [298, 299]. upon [136, 145]. Urbana [321]. ear equations. Ph.D. thesis, University USA [325, 327, 318]. User [323]. using of Toronto, Toronto, ON, Canada, 1958. [301]. Davis:1963:REP

V [176]. [3] Chandler Davis. The rotation of eigen- Validated [329]. Validating [113]. Validat- vectors by a perturbation. I. Jour- REFERENCES 8

nal of Mathematical Analysis and Ap- nal of Mathematical Analysis and Ap- plications, 6:159–173, 1963. CODEN plications, 11:20–27, 1965. CODEN JMANAK. ISSN 0022-247x (print), JMANAK. ISSN 0022-247x (print), 1096-0813 (electronic). See [8, 33]. 1096-0813 (electronic). See [3, 33]. Kahan:1963:ACC Golub:1965:CSV [4] W. Kahan and I. Farkas. Algorithm [9] G. H. Golub and W. Kahan. Calcu- 167: Calculation of confluent divided lating the singular values and pseudo- differences. Communications of the inverse of a matrix. Journal of the So- Association for Computing Machinery, ciety for Industrial and Applied Mathe- 6(4):164–165, April 1963. CODEN matics: Series B, Numerical Analysis,2 CACMA2. ISSN 0001-0782 (print), (2):205–224, ???? 1965. ISSN 0887-459X 1557-7317 (electronic). (print), 1095-7170 (electronic). Kahan:1963:ANIa Kahan:1965:FPO [5] W. Kahan and I. Farkas. Algorithm [10] W. Kahan. The floating-point over/ 169: Newton interpolation with for- underflow trap routine FPTRP.In ward divided differences. Communica- Programmer’s Reference Manual. Insti- tions of the Association for Comput- tute of Computer Science, University ing Machinery, 6(4):165, April 1963. of Toronto, Toronto, Ontario, Canada, CODEN CACMA2. ISSN 0001-0782 1965. LCCN ???? Section 4.1. (print), 1557-7317 (electronic). Kahan:1965:PFR Kahan:1963:ANIb [11] W. Kahan. Pracniques: Further remarks [6] W. Kahan and I. Farkas. Algorithm on reducing truncation errors. Commu- 168: Newton interpolation with back- nications of the Association for Comput- ward divided differences. Communica- ing Machinery, 8(1):40, January 1965. tions of the Association for Comput- CODEN CACMA2. ISSN 0001-0782 ing Machinery, 6(4):165, April 1963. (print), 1557-7317 (electronic). CODEN CACMA2. ISSN 0001-0782 Moller:1965:NQD (print), 1557-7317 (electronic). [12] Ole Møller. Note on quasi double- Kahan:1964:FPM precision. Nordisk tidskrift for infor- [7] W. Kahan and J. J. Leppik. A FOR- mationsbehandling, 5(4):251–255, 1965. TRAN post-mortem procedure. Com- CODEN BITTEL, NBITAB. ISSN munications of the Association for Com- 0006-3835 (print), 1572-9125 (elec- puting Machinery, 7(1):15, January tronic). See [13]. 1964. CODEN CACMA2. ISSN 0001- Moller:1965:QDP 0782 (print), 1557-7317 (electronic). Davis:1965:REP [13] Ole Møller. Quasi double-precision in floating point addition. Nordisk tidskrift [8] Chandler Davis. The rotation of eigen- for informationsbehandling, 5(1):37–50, vectors by a perturbation. II. Jour- 1965. CODEN BITTEL, NBITAB. REFERENCES 9

ISSN 0006-3835 (print), 1572-9125 (elec- trices. Technical report CS42, Depart- tronic). See also [12]. ment of Computer Science, University of California, Berkeley, CA, USA, July 25, Kahan:1966:AES 1966. URL ftp://reports.stanford. [14] W. Kahan. Accurate eigenvalues of a edu/pub/cstr/reports/cs/tr/66/42/ symmetric tri-diagonal matrix. Tech- CS-TR-66-42.pdf. nical Report CS41, Department of Kahan:196x:ACM Computer Science, Stanford University, Stanford, CA, USA, July 22, 1966. ???? [20] W. M. Kahan. Note on bounds for gen- pp. Revised June 1968. erating Bessel functions by recurrence. Kahan:1966:CEB 196x. Kahan:1967:EEB [15] W. M. Kahan. A computable error- bound for systems of ordinary differen- [21] W. M. Kahan. An ellipsoidal error tial equations (abstract). SIAM Review, bound for linear systems of ordinary dif- 8:568–569, 1966. CODEN SIREAD. ferential equations. Report, Computer ISSN 0036-1445 (print), 1095-7200 (elec- Science, University of Toronto, Toronto, tronic). Canada, 1967. ???? pp. Kahan:1966:FIS Kahan:1967:ISS [16] W. Kahan. The FORTRAN IV subrou- [22] W. M. Kahan. 7094-II system sup- tine QDRTC. Technical report, Com- port for numerical analysis. In Proceed- puter library, McLennan Laboratories, ings of the 1967 Army Numerical Anal- University of Toronto, Toronto, ON, ysis Conference (Wisconsin, May 1967), Canada, 1966. pages 175–208 + errata. U.S. Army Re- Kahan:1966:NLA search Office, Research Triangle Park, NC, 1967. LCCN ???? ARO-D Report [17] W. M. Kahan. Numerical linear algebra. 67-3. Reprint of [18]. Canadian mathematical bulletin = Bul- letin canadien de mathématiques, 9(??): Kahan:1967:ITC 757–801, ???? 1966. CODEN CMBUA3. ISSN 0008-4395 (print), 1496-4287 (elec- [23] W. Kahan. Inclusion theorems for clus- tronic). ters of eigenvalues of Hermitian matrices. Report, Computer Science, Univer- Kahan:1966:ISS sity of Toronto, Toronto, Canada, 1967.

[18] W. Kahan. 7094-II system support for Kahan:1967:LMC numerical analysis. SHARE Secretary Distribution 159, C4537, December 12, [24] W. Kahan. Laguerre’s method and a cir- 1966. cle which contains at least one zero of a Kahan:1966:WND polynomial. SIAM Journal on Numer- ical Analysis, 4(3):474–482, September [19] W. Kahan. When to neglect oﬀ-diagonal 1967. CODEN SJNAAM. ISSN 0036- elements of symmetric tri-diagonal ma- 1429 (print), 1095-7170 (electronic). REFERENCES 10

Kahan:1968:CEA Nickel:1969:EBC

[25] W. M. Kahan. Circumscribing an ellip- [30] K. Nickel. Error bounds and computer- soid about the intersection of two ellip- arithmetic. In A. J. H. Morrell, edi- soids. Canadian mathematical bulletin = tor, Proc. of IFIP-Congress 1968, Vol. Bulletin canadien de math´ematiques,11 I, pages 54–60. North-Holland Publ. (??):437–441, ???? 1968. CODEN CM- Comp., Amsterdam, New York, Oxford, BUA3. ISSN 0008-4395 (print), 1496- 1969. Cf.: Kahan, W. M., Invited Com- 4287 (electronic). mentary, Ibidem 60-62. Kahan:1968:FAC Nickel:1969:KBS

[26] W. Kahan. Four aphorisms concerning [31] K. Nickel. Das Kahan-Babuska’sche ﬂoating point hardware design. ACM Summierungsverfahren In Triplex-Algol SIGNUM Newsletter, 3(2):??, July 1968. 60. (German) [The Kahan-Babuˇska CODEN SNEWD6. ISSN 0163-5778 summation method in Triplex-Algol 60]. (print), 1558-0237 (electronic). Interner Bericht Des Inst. F. Informatik 69/3, Universit¨at Karlsruhe, Karlsruhe, Kahan:1968:MCI Germany, 1969. Published in [35].

[27] W. M. Kahan. A more complete inter- Parlett:1969:CPA val arithmetic: Lecture notes for an En- [32] B. N. Parlett and W. Kahan. On the gineering Summer Course in Numerical convergence of a practical QR algorithm. Analysis at the University of Michigan. (With discussion). In Information Pro- Technical report, University of Michi- cessing 68 (Proc. IFIP Congress, Edin- gan, 1968. burgh, 1968), Vol. 1: Mathematics, Soft- Davis:1969:SNB ware, pages 114–118. North-Holland, Amsterdam, 1969. [28] Chandler Davis and W. M. Kahan. Some new bounds on perturbation of sub- Davis:1970:REP spaces. Bulletin of the American Math- [33] Chandler Davis and W. M. Kahan. The ematical Society, 75(4):863–868, ???? rotation of eigenvectors by a perturba- 1969. CODEN BAMOAD. ISSN tion. III. SIAM Journal on Numerical 0002-9904 (print), 1936-881X (elec- Analysis, 7(1):1–46, March 1970. CO- tronic). URL http://projecteuclid. DEN SJNAAM. ISSN 0036-1429 (print), org/euclid.bams/1183530664. 1095-7170 (electronic). See [3, 8]. Kahan:1969:ICC Kahan:1970:ACM [29] W. M. Kahan. Invited commentary [34] W. M. Kahan. Almost-commuting ma- (concerning the invited paper of K. trices are near commuting matrices. Nickel: Error bounds and computer Manuscript, July 23, 1970. arithmetic). In A. Morrell, editor, Proc. Nickel:1970:KBS of IFIP Congress 1968, Vol. I, pages 60– 62. North-Holland Publ. Comp., Ams- [35] K. Nickel. Das Kahan-Babuˇskasche terdam, New York, Oxford, 1969. Summierungsverfahren in Triplex-AL- REFERENCES 11

GOL 60. (German) [The Kahan- ISSN 0163-5778 (print), 1558-0237 (elec- Babuˇska summation method in Triplex- tronic). ALGOL 60]. Zeitschrift für Angewandte Mathematik und Mechanik, 50:369–373, Dorr:1973:REC 1970. CODEN ZAMMAX. ISSN 0044- [41] Fred W. Dorr and Cleve B. Moler. 2267 (print), 1521-4001 (electronic). Roundoff error on the CDC 6600/7600 Kahan:1971:P computers. ACM SIGNUM Newslet- ter, 8(2):24–26, April 1973. CODEN [36] W. Kahan. A problem. ACM SIGNUM SNEWD6. ISSN 0163-5778 (print), Newsletter, 6(3):6, November 1971. CO- 1558-0237 (electronic). See [36] for the DEN SNEWD6. ISSN 0163-5778 (print), original problem. 1558-0237 (electronic). See response [41]. Kahan:1973:EMR Kahan:1971:SEA [42] W. Kahan. Every n × n matrix Z with real spectrum satisfies kZ − Z ∗k≤ [37] W. M. Kahan. A survey of error anal- k ∗k Z + Z (log2 n +0.038). Proceedings ysis. In Freiman et al. [312], pages of the American Mathematical Society, 1214–1239. ISBN 0-7204-2063-6. LCCN 39:235–241, 1973. CODEN PAMYAR. QA76 .I575 1971. URL http://dblp. ISSN 0002-9939 (print), 1088-6826 (elec- uni-trier.de/db/conf/ifip/ifip71- tronic). 2.html#Kahan71. Eight booklets in two volumes. Kahan:1973:IAC Anderson:1972:HHI [43] W. M. Kahan. Implementation of al- [38] Donald G. M. Anderson, Joseph Traub, gorithms (chapter 12). Technical Re- and W. Kahan. How to help an ill-posed port AD 769-124, National Technical In- problem get well. In ACM ’72 [313], page formation Service, Springfield, Virginia, 663. LCCN TK 7885 A84p 1972. The 1973. first annual George Forsythe Memorial Kahan:1973:IAL Lecture, presented by W. Kahan. [44] W. Kahan. Implementation of algo- Kahan:1972:CCC rithms (lecture notes by W. S. Hauge- [39] W. Kahan. Conserving confluence curbs land and D. Hough). Technical Re- ill-condition. Technical Report 6, Com- port 20, Department of Computer Sci- puter Science Department, University of ence, University of California, Berkeley, California, Berkeley, August 1972. ???? CA, USA, 1973. ???? pp. pp. Kahan:1974:ALA Kahan:1972:MHK [45] W. Kahan and B. N. Parlett. An anal- [40] W. Kahan. In memoriam: Hi- ysis of Lanczos algorithms for symmet- rondo Kuki: Apr. 25, 1925–Dec. 28, ric matrices. Technical Report ERL- 1971. ACM SIGNUM Newsletter, 7(1): M467, University of California, Berkeley, 8–10, April 1972. CODEN SNEWD6. Berkeley, CA, USA, 1974. REFERENCES 12

Kahan:1975:EP Kahan:1976:PIP

[46] W. Kahan. An ellipse problem. SIGSAM [50] W. M. Kahan. Pitfalls in ill-posed prob- Bulletin (ACM Special Interest Group lems. SIAM Review, 18(4):810–811, ???? on Symbolic and Algebraic Manipula- 1976. CODEN SIREAD. ISSN 0036- tion), 9(3):11–??, August 1975. CODEN 1445 (print), 1095-7200 (electronic). SIGSBZ. ISSN 0163-5824 (print), 1557- 9492 (electronic). Kahan:1977:CYC

Kahan:1975:SNH [51] W. M. Kahan and B. N. Parlett. Can you count on your calculator? Memo- [47] W. Kahan. Spectra of nearly Hermitian randum UCB/ERL M77/21, Electronics matrices. Proceedings of the American Research Laboratory, College of Engi- Mathematical Society, 48:11–17, 1975. neering, University of California, Berke- CODEN PAMYAR. ISSN 0002-9939 ley, Berkeley, CA, USA, April 6, 1977. ii (print), 1088-6826 (electronic). + 28 pp. URL http://www.math.utah. edu/pub/bibnet/authors/k/kahan- Laveuve:1975:DKA william-m.bib; http://www.math. utah.edu/pub/bibnet/subjects/acc- [48] S. E. Laveuve. Definition Einer Kahan- stab-num-alg.bib. German Transl. Arithmetik Und Ihre Implementierung. Published In: Jahrbuch Uberblicke¨ (German) [Definition of a Kahan arith- Mathematik 1978, Ed. by B. Fuchssteiner metic and its implementation]. In Nickel and others, Bibliographisches Institut, [314], pages 236–245. CODEN LNCSD9. Mannheim-Wien-Zürich, 199–216, 1978. ISBN 0-387-07170-9. ISSN 0302- 9743 (print), 1611-3349 (electronic). Kahan:1977:NSC LCCN QA297 .I541. DM30.00. URL http://link.springer-ny.com/link/ [52] W. Kahan. And now for something com- service/series/0558/tocs/t0029. pletely different: The Texas Instruments htm; http://www.springerlink. SR-52. Memorandum No. UCB/ERL com/content/978-0-387-07170-1; M77/23, Electronics Research Labora- http://www.springerlink.com/openurl. tory, College of Engineering, University asp?genre=issue&issn=0302-9743& of California, Berkeley, April 1977. ???? volume=29; https://link.springer. pp. com/book/10.1007/3-540-07170-9. Ger- man or English. Lauer:1977:SKP

Kahan:1976:HFS [53] Markus Lauer. A solution to Ka- han’s problem (SIGSAM problem no. [49] W. Kahan and B. N. Parlett. How far 9). SIGSAM Bulletin (ACM Special should you go with the Lanczos process? Interest Group on Symbolic and Alge- In Bunch and Rose [315], pages 131– braic Manipulation), 11(2):16–20, ???? 144. ISBN 0-12-141050-1. LCCN QA188 1977. CODEN SIGSBZ. ISSN 0163-5824 .S989 1975. (print), 1557-9492 (electronic). REFERENCES 13

Kahan:1978:HFS Gentleman [316], pages 32–36. LCCN QA276.4. [54] W. Kahan and B. N. Parlett. How far should you go with the Lanczos process? Kahan:1979:PFP Memorandum UCB/ERL M78/48, Elec- [59] W. Kahan and J. Palmer. On a proposed tronics Research Laboratory, College of ﬂoating-point standard. ACM SIGNUM Engineering, University of California, Newsletter, 14(3S (Special issue)):13– Berkeley, Berkeley, CA, USA, 1978. 16 21, October 1979. CODEN SNEWD6. pp. ISSN 0163-5778 (print), 1558-0237 (elec- Kahan:1978:KSI tronic).

[55] W. Kahan and B. N. Parlett. Können Sie Kahan:1980:AEG sich auf Ihren Rechner verlassen? (Ger- [60] W. Kahan. Aitken’s extrapolation and man) [can you count on your calcula- Gaussian quadrature. IEEE Floating- ¨ tor?]. Jahrbuch Uberblicke Mathematik, Point Subcommittee Working Docu- ??:199–216, 1978. ment P754/80-1.19, 1980. Coonen:1979:PSB Kahan:1980:HCE [56] Jerome Coonen, William Kahan, John [61] William M. Kahan. Handheld cal- Palmer, Tom Pittman, and David culator evaluates integrals. Hewlett- Stevenson. A proposed standard for bi- Packard Journal: technical information nary floating point arithmetic: Draft from the laboratories of Hewlett-Packard 5.11. ACM SIGNUM Newsletter,14 Company, 31(8):23–32, August 1980. (3S (Special issue)):4–12, October 1979. CODEN HPJOAX. ISSN 0018-1153. CODEN SNEWD6. ISSN 0163-5778 URL http://www.cs.berkeley.edu/~ (print), 1558-0237 (electronic). wkahan/Math128/INTGTkey.pdf. Lec- ture notes for Math 128. Kahan:1979:PCK Kahan:1980:IAO [57] William M. Kahan. Personal calculator has key to solve any equation [62] William M. Kahan. Interval arithmetic f(x)=0. Hewlett-Packard Jour- options in the proposed IEEE Floating nal: technical information from the Point Arithmetic Standard. In Nickel laboratories of Hewlett-Packard Com- [317], pages 99–128. ISBN 0-12-518850- pany, 30(12):20–26, December 1979. 1. LCCN QA297.75 .I57 1980. CODEN HPJOAX. ISSN 0018-1153. Kahan:1980:SPI URL http://www.cs.berkeley.edu/~ √ wkahan/Math128/SOLVEkey.pdf. Lec- [63] W. Kahan. Software x for the ture notes for Math 128. proposed IEEE floating-point standard. Manuscript, August 25, 1980. Kahan:1979:PIC Laveuve:1980:DKA [58] W. Kahan, J. Palmer, and J. Coo- nen. Proposed IEEE-CS Standard for [64] S. E. Laveuve. Definition Einer Kahan- Binary Floating Point Arithmetic. In Arithmetik Und Ihre Implementierung REFERENCES 14

In Tripleo. (German) [Deﬁnition of a Mathematics, University of California, Kahan Arithmetic and its implementa- Berkeley, CA, USA, October 1982. tion in Tripleo]. Academic Press, New Kahan:1982:NOS York, NY, USA, 1980. 355–366 pp. [70] W. Kahan and Jerome T. Coonen. The Kahan:1981:PEC near orthogonality of syntax, semantics, [65] W. Kahan. The programming envi- and diagnostics in numerical program- ronment’s contribution to program ro- ming environments. In Reid [318], pages bustness. ACM SIGNUM Newsletter, 103–115. ISBN 0-444-86377-X. LCCN 16(4):10–??, October 1981. CODEN QA297 .I34 1981. SNEWD6. ISSN 0163-5778 (print), Kahan:1982:RBA 1558-0237 (electronic). [71] W. Kahan, B. N. Parlett, and E. Jiang. Kahan:1981:WDW Residual bounds on approximate eigen- [66] W. Kahan. Why do we need a ﬂoating- systems of nonnormal matrices. SIAM point arithmetic standard? Technical Journal on Numerical Analysis, 19(3): report, University of California, Berke- 470–484, June 1982. CODEN SJNAAM. ley, CA, USA, February 12, 1981. 41 ISSN 0036-1429 (print), 1095-7170 (elec- pp. tronic). Neumann:1981:KRC Waser:1982:IAD [72] Shlomo Waser and Michael J. Flynn. In- [67] M. Neumann. The Kahan S.O.R. con- troduction to Arithmetic for Digital Sys- vergence bound for nonsingular and ir- tems Designers. Holt, Rinehart and reducible M-matrices. Linear Algebra Winston, New York, 1982. ISBN 0- and its Applications, 39:205–222, 1981. 03-060571-7. xvii + 308 pp. LCCN CODEN LAAPAW. ISSN 0024-3795 TK7895.A65 W37 1982. (print), 1873-1856 (electronic). Kahan:1983:M Davis:1982:NPD [73] W. Kahan. Minimizing q × m − [68] Chandler Davis, W. M. Kahan, and n. Technical report, Department of H. F. Weinberger. Norm-preserving di- Mathematics and Department of Elec- lations and their applications to optimal trical Engineering and Computer Sci- error bounds. SIAM Journal on Nu- ence, University of California, Berke- merical Analysis, 19(3):445–469, June ley, Berkeley, CA, USA, March 1983. 1982. CODEN SJNAAM. ISSN 0036- URL http://www.cs.berkeley.edu/~ 1429 (print), 1095-7170 (electronic). See wkahan/testpi/nearpi.c. [86]. Kahan:1983:MWS Kahan:1982:BCC [74] W. Kahan. Mathematics written in [69] W. Kahan. Branch cuts for complex el- sand — the HP-15C, Intel 8087, etc. ementary functions. Technical Report In Anonymous [319], pages 12–26. PAM-105, Center for Pure and Applied ISBN ???? ISSN 0149-9963. LCCN REFERENCES 15

QA276.4 .A43a. URL http://www. 0163-5778 (print), 1558-0237 (elec- cs.berkeley.edu/~wkahan/MathSand. tronic). pdf. Kahan:1985:AIA Kahan:1983:PISa [80] W. Kahan and E. LeBlanc. Anoma- [75] W. Kahan. The proposed IEEE Stan- lies in the IBM ACRITH pack- dard p754 for Floating-Point Arith- age. In Hwang [321], pages 322– metic: What good is it? Manuscript, 331. ISBN 0-8186-0632-0 (paper- 1983. back), 0-8186-8632-4 (hard), 0-8186- Kahan:1983:PISb 4632-2 (microfiche). LCCN QA76.9.C62 S95 1985. URL http://www.acsel- [76] W. Kahan. The proposed IEEE Stan- lab.com/arithmetic/arith7/papers/ dard p754 for Floating-Point Arith- ARITH7_Kahan_LeBlanc.pdf. metic: What good is it? In IEEE [320], Kahan:1985:MSC page ?? [81] W. Kahan. On the monotonicity of some Ozawa:1983:AIK computed functions. Technical Report [77] K. Ozawa. Analysis and improvement of PAM-261, Center for Pure and Applied Kahan’s summation algorithm. Journal Mathematics, University of California, of Information Processing (of Japan??), Berkeley, CA, USA, January 1985. 6(4):226–230, 1983. Kahan:1986:DVB Cody:1984:PRW [82] W. Kahan. Decimal versus binary [78] William J. Cody, Jr., Jerome T. floating-point arithmetic. Manuscript, Coonen, David M. Gay, K. Hanson, November 12, 1986. David Hough, W. Kahan, R. Karpin- Kahan:1986:RAF ski, John F. Palmer, F. N. Ris, and D. Stevenson. A proposed radix- and [83] W. Kahan. Rational arithmetic in word-length-independent standard for floating-point. Technical Report PAM- floating-point arithmetic. IEEE Micro,4 343, Center for Pure and Applied Math- (4):86–100, July/August 1984. CODEN ematics, University of California, Berke- IEMIDZ. ISSN 0272-1732 (print), 1937- ley, CA, USA, September 1986. 8 pp. 4143 (electronic). Kahan:1986:RPE Cody:1985:PRW [84] W. Kahan. Roundoff in polynomial eval- [79] W. J. Cody, J. T. Coonen, D. M. uation. Manuscript, November 16, 1986. Gay, K. Hanson, D. Hough, W. Ka- Kahan:1986:SRC han, R. Karpinski, J. Palmer, F. N. Ris, and D. Stevenson. A proposed radix- [85] W. Kahan. To solve a real cubic and word-length-independent standard equation. Technical Report PAM-352, for floating-point arithmetic. ACM Center for Pure and Applied Mathe- SIGNUM Newsletter, 20(1):37–51, Jan- matics, University of California, Berke- uary 1985. CODEN SNEWD6. ISSN ley, CA, USA, November 1986. 20 REFERENCES 16

pp. URL http://www.eecs.berkeley. Kahan:1987:HSM edu/~wkahan/Math128/Cubic.pdf. [91] W. Kahan. How should Max and Min be Meinguet:1986:DKW deﬁned? Manuscript, August 19, 1987.

[86] Jean Meinguet. On the Davis-Kahan- Kahan:1987:PCF Weinberger solution of the norm- preserving dilation problem. Nu- [92] W. Kahan. Presubstitution and contin- merische Mathematik, 49(2/3):331–341, ued fractions. Manuscript, March 17, July 1986. CODEN NUMMA7. ISSN 1987. 0029-599X (print), 0945-3245 (elec- Demmel:1988:CSS tronic). Refers to the work [68]. [93] J. Demmel and W. Kahan. Com- Fateman:1987:IEI puting small singular values of bidi- [87] Richard J. Fateman and W. Kahan. agonal matrices with guaranteed high Improving exact integrals from sym- relative accuracy. LAPACK Working bolic algebra systems. Technical Re- Note 03, Mathematics and Computer port PAM-261, Center for Pure and Ap- Science Division, Argonne National Lab- plied Mathematics, University of Cal- oratory, 9700 South Cass Avenue, Ar- ifornia, Berkeley, CA, USA, August gonne, IL 60439-4801, USA, February 1987. URL http://www.cybertester. 1988. URL http://www.netlib.org/ com/data/iintegr.pdf. lapack/lawns/lawn03.ps; http:/ /www.netlib.org/lapack/lawnspdf/ Kahan:1987:BCC lawn03.pdf. ANL, MCS-TM-110, February 1988. [88] W. Kahan. Branch cuts for complex elementary functions or much ado about Kahan:1988:CPA nothing’s sign bit. In Iserles and Pow- ell [322], pages 165–211. ISBN 0-19- [94] W. Kahan. A computer program with 853614-3. LCCN QA297.J65 1986. URL almost no significance. Manuscript, http://people.freebsd.org/~das/ November 9, 1988. kahan86branch.pdf; http://www. Kahan:1988:TWB cs.berkeley.edu/~dbindel/class/ cs279/. [95] W. Kahan. To test whether binary Kahan:1987:CWF floating-point multiplication is correctly rounded. Manuscript, July 1988. [89] W. Kahan. Checking whether floating- point division is correctly rounded. Lec- Lenstra:1988:PT ture notes., 1987. [96] H. W. Lenstra, Jr. Probability the- Kahan:1987:DPI ory. World-Wide Web document, November 1988. URL http://www. [90] W. Kahan. Doubled-precision IEEE cs.berkeley.edu/~wkahan/Math55/ standard 754 floating-point arithmetic. Lenstra.pdf. Lecture notes for Math Manuscript, February 26, 1987. 55. REFERENCES 17

Kahan:1989:CAA and Statistical Computing, 11(5):873– 912, September 1990. CODEN SIJCD4. [97] W. Kahan. Calculating area and angle of ISSN 0196-5204. a needle-like triangle. Manuscript, Jan- Kahan:1990:BPA uary 26, 1989. Kahan:1989:OFH [103] W. Kahan. Better to prescribe arithmetic than describe it. Technical re- [98] W. Kahan. The occasional futility of port, Department of Computer Science, higher-precision arithmetic. Manuscript, University of California, Berkeley, CA, September 28, 1989. USA, February 21, 1990. Turing Award Lecture presented at ACM Conference, Kahan:1989:PCA Washington. [99] W. Kahan. Paradoxes in concepts of ac- Kahan:1990:HCA curacy. Lecture notes from Joint Semi- nar on Issues and Directions in Scientific [104] W. Kahan. How Cray’s arithmetic Computation, Berkeley, 1989. hurts scientific computation (and what might be done about it). In CUG [323], Kahan:1989:SRN page 42. ISBN ???? LCCN ???? URL [100] W. Kahan. A singularity removable http://754r.ucbtest.org/issues/ numerically when arithmetic is clean. cray-hurts-uk.pdf; http://754r. Manuscript, May 17, 1989. ucbtest.org/issues/cray-hurts-ut. pdf; http://754r.ucbtest.org/ Anderson:1990:PEL issues/cray-hurts.pdf. Manuscript [101] E. Anderson, C. Bischof, J. Demmel, prepared for the Cray User Group meet- J. Dongarra, J. Du Croz, S. Hammar- ing in Toronto, Canada, April 10, 1990. ling, and W. Kahan. Prospectus for an Kahan:1990:PCA extension to LAPACK: A portable linear algebra library for high-performance [105] William Kahan. Paradoxes in concepts computers. LAPACK Working Note of accuracy, 1990. 1 videocassette (60 and Computer Science Dept. Techni- min.). cal Report 26 and CS-90-118, Depart- Kahan:1990:POC ment of Computer Science, Univer- sity of Tennessee, Knoxville, Knoxville, [106] W. Kahan. Paradoxes in our concepts TN 37996, USA, November 1990. 10 of computational accuracy. Manuscript, pp. URL http://www.netlib.org/ October 1, 1990. lapack/lawns/lawn26.ps; http:/ Kahan:1990:TCC /www.netlib.org/lapack/lawnspdf/ lawn26.pdf. LAPACK Working Note [107] W. Kahan. Twenty challenges for #26. UT-CS-90-118, November 1990. computerized symbolic algebra systems. Manuscript, August 16, 1990. Demmel:1990:ASV Demmel:1991:DPHa [102] James W. Demmel and W. Kahan. Ac- curate singular values of bidiagonal ma- [108] James Demmel, Jack Dongarra, and trices. SIAM Journal on Scientific W. Kahan. On designing portable high REFERENCES 18

performance numerical libraries. LA- Paxson:1991:PTI PACK Working Note 39, Department of Computer Science, University of Ten- [114] Vern Paxson and W. Kahan. A pro- nessee, Knoxville, Knoxville, TN 37996, gram for testing IEEE binary–decimal USA, July 1991. URL http://www. conversion. World-Wide Web document, netlib.org/lapack/lawns/lawn39. May 1991. URL ftp://ftp.ee.lbl. ps; http://www.netlib.org/lapack/ gov/testbase-report.ps.Z; ftp:/ lawnspdf/lawn39.pdf. UT-CS-91-141, /ftp.ee.lbl.gov/testbase.tar.Z. July, 1991. Demmel:1992:DPH Demmel:1991:DPHb [115] James W. Demmel, J. J. Dongarra, [109] J. Demmel, J. Dongarra, and W. Ka- and W. Kahan. On designing portable han. On designing portable high perfor- high performance numerical libraries. In mance numerical libraries. In Griffiths D. F. Griffiths and G. A. Watson, ed- and Watson [324], page ?? ISBN 0-582- itors, Numerical Analysis 1991, Pro- 08908-5. LCCN QA297 .D85 1991. ceedings of the 14th Dundee Conference, volume 260 of Pitman Research Notes Kahan:1991:APL in Mathematics, pages 69–84. Longman Scientific and Technical, Harlow, Essex, [110] William Kahan and J. W. Thomas. Aug- UK, 1992. menting a programming language with complex arithmetic. Technical Report Kahan:1992:ARL NCEG/91-039, UCB/CSD 91/667, De- partment of Computer Science, Univer- [116] W. Kahan. Analysis and refutation of sity of California, Berkeley, CA, USA, the LCAS. ACM SIGPLAN Notices,27 November 15, 1991. 8 pp. Manuscript. (1):61–74, January 1992. CODEN SIN- ODQ. ISSN 0362-1340 (print), 1523- Kahan:1991:ARL 2867 (print), 1558-1160 (electronic).

[111] W. Kahan. Analysis and refutation of Kahan:1992:DCD the LCAS. ACM SIGNUM Newslet- ter, 26(3):2–15, July 1991. CODEN [117] W. Kahan. DAYDATE: Computing SNEWD6. ISSN 0163-5778 (print), days between dates, the day of the 1558-0237 (electronic). week, etc. World-Wide Web document, September 16, 1992. URL http://www. Kahan:1991:CMA cs.berkeley.edu/~wkahan/daydate/.

[112] W. Kahan. Contracted multiply-adds. Kahan:1992:FPE Manuscript, September 20, 1991. [118] W. Kahan. Floating-point exception- Kahan:1991:VTC handling. Manuscript, July 31, 1992. [113] W. Kahan. Validating/testing/ Kahan:1992:NLI conﬁrming/checking/correcting numerical software. Manuscript, November 26, [119] W. Kahan. Notes on Laguerre’s itera- 1991. tion. Manuscript, December 4, 1992. REFERENCES 19

Kahan:1992:RCM Kahan:1994:CBV

[120] W. Kahan. Roundoﬀ in complex mul- [127] W. Kahan. Computer benchmarks ver- tiplication. Manuscript, November 11, sus accuracy. Draft manuscript, June 1992. 1994. Kahan:1992:WN Kahan:1994:W [128] W. Kahan. When is x∗[1/x] < x/x =1? [121] W. Kahan. What numbers? Manu- Manuscript, January 1, 1994. script, September 9, 1992. Sanz-Serna:1994:USI Kahan:1993:AAS [129] J. M. Sanz-Serna. An unconventional [122] W. Kahan. Analysis and application of symplectic integrator of W. Kahan. Ap- simply compensated summation. Manu- plied Numerical Mathematics: Transac- script, September 7, 1993. tions of IMACS, 16(1–2):245–250, De- Kahan:1993:TIE cember 1, 1994. CODEN ANMAEL. ISSN 0168-9274 (print), 1873-5460 (elec- [123] W. Kahan. A tridiagonal inverse eigen- tronic). URL http://www.elsevier. problem and the travails of a would-be com/cgi-bin/cas/tree/store/apnum/ portable programmer. Manuscript, June cas_sub/browse/browse.cgi?year= 1, 1993. 1994&volume=16&issue=1-2&aid=506. A Festschrift to honor Professor Robert Ozawa:1993:SAE Vichnevetsky on his 65th birthday. [124] K. Ozawa and M. Miyazaki. A sum- Woehr:1994:LVP mation algorithm with error correction [130] Jack Woehr. Lotﬁ visions, part 2. Dr. for parallel computers. Systems and Dobb’s Journal of Software Tools, 19(8): Computers in Japan, 24(7):62–68, ???? 52–??, August 1994. CODEN DDJOEB. 1993. CODEN SCJAEP. ISSN 0882- ISSN 1044-789X. 1666 (print), 1520-684X (electronic). See [11]. Kahan:1995:LNS

Axler:1994:DD [131] W. Kahan. Lecture notes on the status of IEEE Standard 754 for binary [125] Sheldon Axler. Down with determi- ﬂoating-point arithmetic. Manuscript, nants! World-Wide Web document, May 23, 1995. December 21, 1994. URL http://www. Kahan:1995:TSD cs.berkeley.edu/~wkahan/MathH110/ DownDets.pdf. Lecture notes for Math [132] W. Kahan. A test for SRT division. Lec- H110. ture notes, 1995. URL http://www.cs. Kahan:1994:AS berkeley.edu/~wkahan/srtest. Kahan:1995:USP [126] W. Kahan. On the advantages of the 8087’s stack. Manuscript, August 23, [133] Students of Prof. W. Kahan. UCB- 1994. TEST: a suite of programs for test- REFERENCES 20

ing certain difficult cases of IEEE 754 URL http://www.cs.berkeley.edu/~ floating-point arithmetic. World-Wide wkahan/ieee754status/baleful.ps. Web document, March 12, 1995. URL http://www.netlib.org/fp/ucbtest. Kahan:1996:BN tgz. [137] W. Kahan. Beastly numbers. World- Cao:1996:SVK Wide Web document., January 13, 1996. URL [134] Zhi hao Cao, Jin jun Xie, and Ren- http://www.cs.berkeley.edu/ Cang Li. A sharp version of Ka- ~wkahan/tests/; http://www.cs. han’s theorem on clustered eigenval- berkeley.edu/~wkahan/tests/numbeast. . ues. Linear Algebra and its Ap- ps plications, 245(1–3):147–155, Septem- Kahan:1996:CAN ber 15, 1996. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (elec- [138] W. Kahan. A computation with al- tronic). URL http://www.elsevier. most no significance. Report, Depart- com/cgi-bin/cas/tree/store/laa/ ment of Mathematics and Department cas_sub/browse/browse.cgi?year= of Electrical Engineering and Computer 1996&volume=245&issue=1-3&aid=9400226. Science, University of California, Berke- Goldreich:1996:HCC ley, Berkeley, CA, USA, May 6, 1996. 8 pp. URL http://www.eecs.berkeley. [135] Oded Goldreich and Ariel Kahan. edu/~wkahan/CS279/Div754.pdf. How to construct constant-round zero- knowledge proof systems for NP. Jour- Kahan:1996:IPE nal of Cryptology: the journal of the International Association for Crypto- [139] W. Kahan. The improbability of prob- logic Research, 9(3):167–189, Summer abilistic error analyses for numerical 1996. CODEN JOCREQ. ISSN computations. Manuscript. This is an 0933-2790 (print), 1432-1378 (elec- extended version of transparencies ti- tronic). URL http://link.springer. tled “The Improbability of Probabilis- de/link/service/journals/00145/ tic Error Analysis”, first presented in bibs/9n3p167.html; http://link. Hamburg at the third ICIAM Congress, springer.de/link/service/journals/ 3–7 July, 1995., February 28, 1996. 00145/bibs/9n3p167.pdf; http:/ URL http://www.cs.berkeley.edu/~ /link.springer.de/link/service/ wkahan/improber.ps. journals/00145/bibs/9n3p167.tex; http://link.springer.de/link/service/ Kahan:1996:LNS journals/00145/tocs/00903.html. Kahan:1996:BEC [140] W. Kahan. Lecture notes on the status of IEEE Standard 754 for bi- [136] W. Kahan. The baleful effect of nary floating-point arithmetic. World- computer benchmarks upon applied Wide Web document., May 1996. mathematics, physics, and chemistry. URL http://www.cs.berkeley.edu/~ World-Wide Web document., 1996. wkahan/ieee754status/ieee754.ps. REFERENCES 21

Kahan:1996:TCR World-Wide Web document., July 15, 1997. URL http://www.cs.berkeley. [141] W. Kahan. A test for correctly edu/~wkahan/SIAMjvnl.ps. Presented rounded SQRT. Lecture notes., 1996. at the SIAM 45th annual meeting, Stan- URL http://www.cs.berkeley.edu/~ ford University. wkahan/SQRTest.ps. Kahan:1997:LNS Kahan:1996:WCY [146] W. Kahan. Lecture notes on the [142] W. Kahan. What can you learn about status of IEEE Standard 754 for Bi- floating-point arithmetic in one hour? nary Floating-Point Arithmetic. World- Postscript version accessible electron- Wide Web document, October 1, 1997. ically at http://http.cs.berkeley. URL http://www.cs.berkeley.edu/~ edu/~wkahan/ieee754status., 1996. wkahan/ieee754status/IEEE754.PDF. URL http://www.cs.berkeley.edu/~ wkahan/ieee754status/cs267fp.ps. Kahan:1997:MAA Zheng:1996:FSG [147] W. Kahan. Miscalculating area and angles of a needle-like triangle. Manu- [143] Dao-Sheng Zheng. Further study and script, July 1997. generalization of Kahan’s matrix exten- Kahan:1997:RDI sion theorem. SIAM Journal on Ma- trix Analysis and Applications, 17(3): [148] W. Kahan and Melody Y. Ivory. Round- 621–631, July 1996. CODEN SJMAEL. off degrades an idealized cantilever. ISSN 0895-4798 (print), 1095-7162 (elec- Technical report, Department of Mathe- tronic). See note [175]. matics and Department of Electrical En- Kahan:1997:CCR gineering and Computer Science, Uni- versity of California, Berkeley, Berke- [144] William Kahan and Ren-Cang Li. Com- ley, CA, USA, July 3, 1997. 11 pp. position constants for raising the orders URL http://www.cs.berkeley.edu/ of unconventional schemes for ordinary ~wkahan/Cantilever.pdf; http:// differential equations. Mathematics of www.cs.berkeley.edu/~wkahan/Cantilever. Computation, 66(219):1089–1099, July ps. 1997. CODEN MCMPAF. ISSN 0025- Kahan:1997:USC 5718 (print), 1088-6842 (electronic). URL http://www.ams.org/jourcgi/ [149] William Kahan and Ren-Chang Li. Un- jour-pbprocess?fn=110&arg1=S0025- conventional schemes for a class of ordi- 5718-97-00873-9&u=/mcom/1997-66- nary differential equations—with appli- 219/. cations to the Korteweg–de Vries equa- Kahan:1997:JNL tion. Journal of computational physics, 134(2):316–331, July 1, 1997. CO- [145] W. Kahan. The John von Neumann lec- DEN JCTPAH. ISSN 0021-9991 (print), ture on the baleful effect of computer 1090-2716 (electronic). URL http: languages and benchmarks upon applied //www.sciencedirect.com/science/ mathematics, physics and chemistry. article/pii/S0021999197957107. REFERENCES 22

Wo ehr:1997:CWK Wide Web document, October 24, 1998. URL http://www.cs.berkeley.edu/~ [150] Jack Woehr. A conversation with wkahan/MathH110/chio.pdf. Lecture William Kahan: How important is nu- notes for Math H110. merical accuracy? Dr. Dobb’s Jour- Kahan:1998:DP nal of Software Tools, 22(11):18–20, 22, 24, 26, 30, 32, November 1997. CO- [155] W. Kahan. Diagonal prominence. DEN DDJOEB. ISSN 1044-789X. Ka- World-Wide Web document, Octo- han, the father of the IEEE 754 floating- ber 25, 1998. URL http://www. point standard, talks about floating- cs.berkeley.edu/~wkahan/MathH110/ point arithmetic issues, and numerical diagprom.pdf. Lecture notes for Math deficiencies in Java. H110. Xie:1997:NDK Kahan:1998:GEO [151] Jianjun Xie. A note on the Davis- [156] W. Kahan. Geometry of elementary op- Kahan sin Θ theorem. Linear Algebra erations. World-Wide Web document, and its Applications, 258(1–3):129–135, September 22, 1998. URL http://www. June ??, 1997. CODEN LAAPAW. cs.berkeley.edu/~wkahan/MathH110/ ISSN 0024-3795 (print), 1873-1856 (elec- geo.pdf. Lecture notes for Math H110. tronic). URL http://www.elsevier. Kahan:1998:GJI com/cgi-bin/cas/tree/store/laa/ cas_sub/browse/browse.cgi?year= [157] W. Kahan. Gauss–Jordan inversion of 1997&volume=258&issue=1-3&aid=9600207. a matrix. World-Wide Web document, Darcy:1998:APE October 16, 1998. URL http://www. cs.berkeley.edu/~wkahan/MathH110/ [152] Joseph D. Darcy and William Kahan. gji.pdf. Lecture notes for Math H110. Analysis of Proposal for Extension to Kahan:1998:HJFa Java Floating Point Semantics, Revision 1. Technical report, Java Grande Nu- [158] W. Kahan and Joseph D. Darcy. merics Working Group, August 7, 1998. How Java’s floating-point hurts ev- 18 pp. URL http://www.sonic.net/~ eryone everywhere. Technical re- jddarcy/Research/jgrande.pdf. port, Department of Mathematics and Department of Electrical Engineer- Kahan:1998:AFE ing and Computer Science, Univer- [153] W. Kahan. Answers for final examina- sity of California, Berkeley, Berkeley, tion. World-Wide Web document, De- CA, USA, June 18, 1998. 80 pp. cember 19, 1998. URL http://www. URL http://www.cs.berkeley.edu/ cs.berkeley.edu/~wkahan/MathH110/ ~wkahan/JAVAhurt.pdf; http:// finexms.pdf. Lecture notes for Math www.cs.berkeley.edu/~wkahan/JAVAhurt. H110. ps. Kahan:1998:CTL Kahan:1998:HJFb [154] W. Kahan. Chió’s trick for linear equa- [159] William Kahan. How Java’s floating- tions with integer coefficients. World- point hurts everyone everywhere. In REFERENCES 23

ACM [326], page ?? CODEN CPEXEI. Kahan:1998:LSA ISSN 1040-3108 (print), 1096-9128 (electronic). LCCN ???? URL http://www. [164] W. Kahan. Least-squares approxima- cs.ucsb.edu/conferences/java98/ tion and bilinear forms. World-Wide papers/javahurt.pdf. Also published Web document, September 20, 1998. as Concurrency: Practice and Experi- URL http://www.cs.berkeley.edu/~ ence, 10(11–13), September 1998, CO- wkahan/MathH110/lstsqrs.pdf. Lec- DEN CPEXEI, ISSN 1040-3108. ture notes for Math H110. Kahan:1998:IPE Kahan:1998:MLN [160] W. Kahan. The improbability of proba- [165] W. Kahan. Matlab’s loss is no- bilistic error analyses for numerical com- body’s gain. Technical report, De- putations. Technical report, Depart- partment of Mathematics and De- ment of Mathematics and Department partment of Electrical Engineering of Electrical Engineering and Computer and Computer Science, University of Science, University of California, Berke- California, Berkeley, Berkeley, CA, ley, Berkeley, CA, USA, June 10, 1998. USA, August 23, 1998. 35 pp. 34 pp. URL http://www.cs.berkeley. URL http://www.cs.berkeley.edu/ edu/~wkahan/improber.pdf. ~wkahan/MxMulEps.pdf; http:// www.cs.berkeley.edu/~wkahan/MxMulEps. Kahan:1998:JFD ps. [161] W. Kahan. Jacobi’s formula for the Kahan:1998:NDS derivative of a determinant. World- Wide Web document, October 14, 1998. [166] W. Kahan. Notes on 2-dimensional URL http://www.cs.berkeley.edu/~ spaces. World-Wide Web document, wkahan/MathH110/jacobi.pdf. Lec- October 4, 1998. URL http://www. ture notes for Math H110. cs.berkeley.edu/~wkahan/MathH110/ Kahan:1998:LNR 2dspaces.pdf. Lecture notes for Math H110. [162] W. Kahan. Lecture notes on real root- ﬁnding. World-Wide Web document, Kahan:1998:PSP March 4, 1998. URL http://www. cs.berkeley.edu/~wkahan/Math128/ [167] W. Kahan. Problem set 1: Prob- LNRRabst.txt. Lecture notes for Math lems about our axioms for a vector 128. space. World-Wide Web document, September 16, 1998. URL http://www. Kahan:1998:LRR cs.berkeley.edu/~wkahan/MathH110/ [163] W. Kahan. A lecture on real root- prblms1.pdf. Lecture notes for Math ﬁnding. World-Wide Web document, H110. April 6, 1998. URL http://www. Kahan:1998:RRE cs.berkeley.edu/~wkahan/Math128/ LecRlRtF.pdf. Lecture notes for Math [168] W. Kahan. The reduced row- 128. Extracted from “Lecture Notes on echelon form is unique. World-Wide Real Root-Finding” [162]. Web document, September 12, 1998. REFERENCES 24

URL http://www.cs.berkeley.edu/~ Severance:1998:SII wkahan/MathH110/RREF1.pdf. Lecture notes for Math H110. [174] Charles Severance. Standards: IEEE Kahan:1998:SPS 754: An interview with William Kahan. Computer, 31(3):114–115, March 1998. [169] W. Kahan. Solutions for problem set 2. CODEN CPTRB4. ISSN 0018-9162 World-Wide Web document, October 1, (print), 1558-0814 (electronic). URL 1998. URL http://www.cs.berkeley. http://pdf.computer.org/co/books/ edu/~wkahan/MathH110/prblms2.pdf. co1998/pdf/r3114.pdf. Lecture notes for Math H110. Zheng:1998:NFS Kahan:1998:THT

[170] W. Kahan. Take-home test’s solu- [175] Dao-Sheng Zheng. Note on “Fur- tions. World-Wide Web document, ther Study and Generalization of Ka- October 5, 1998. URL http://www. han’s Matrix Extension Theorem”. cs.berkeley.edu/~wkahan/MathH110/ SIAM Journal on Matrix Analysis and tkhms.pdf. Lecture notes for Math Applications, 19(1):277–278, January H110. 1998. CODEN SJMAEL. ISSN 0895- 4798 (print), 1095-7162 (electronic). Kahan:1998:TPS URL http://epubs.siam.org/sam- bin/dbq/article/31443. See [143]. [171] W. Kahan. Test problems and solutions. World-Wide Web document, De- Anonymous:1999:AAM cember 4, 1998. URL http://www. cs.berkeley.edu/~wkahan/MathH110/ [176] Anonymous. ACM Alan M. Turing testexam.pdf. Lecture notes for Math Award: William V. Kahan. World Wide H110. Web document, February 8, 1999. URL Kahan:1998:VSB http://www.acm.org/awards/turing_ citations/kahan.html. [172] W. Kahan. Vector spaces, bases, and dual spaces. World-Wide Web docu- Kahan:1999:C ment, November 4, 1998. URL http:// www.cs.berkeley.edu/~wkahan/MathH110/[177] W. Kahan. Computing xn. World- pts.pdf. Lecture notes for Math H110. Wide Web document, March 20, 1999. URL http://www.cs.berkeley.edu/~ Severance:1998:IOM wkahan/Math55/npower.pdf. Lecture notes for Math 55. [173] Charles Severance. An interview with the old man of ﬂoating-point. Remi- Kahan:1999:CS niscences elicited from William Kahan. World-Wide Web document., February [178] W. Kahan. Coins and stamps. World- 1998. URL http://www.cs.berkeley. Wide Web document, May 1, 1999. edu/~wkahan/ieee754status/754story. URL http://www.cs.berkeley.edu/~ html. A shortened version appears in wkahan/Math55/coins.pdf. Lecture [174]. notes for Math 55. REFERENCES 25

Kahan:1999:CSC Kahan:1999:EMSa

[179] W. Kahan. Conic sections in [185] W. Kahan. Exam model solutions. the complex z-plane. World-Wide World-Wide Web document, Febru- Web document, September 4, 1999. ary 10, 1999. URL http://www. URL http://www.cs.berkeley.edu/~ cs.berkeley.edu/~wkahan/Math55/ wkahan/Math185/conics.pdf. Lecture feb10s.pdf. Lecture notes for Math 55. notes for Math 185. Kahan:1999:EMSb Kahan:1999:CSL [186] W. Kahan. Exam: Model solutions. [180] W. Kahan. California super lottery. World-Wide Web document, March 3, World-Wide Web document, April 13, 1999. URL http://www.cs.berkeley. 1999. URL http://www.cs.berkeley. edu/~wkahan/Math55/m55mar3s.pdf. edu/~wkahan/Math55/lotto.pdf. Lec- Lecture notes for Math 55. ture notes for Math 55. Kahan:1999:EMSc Kahan:1999:CVC [187] W. Kahan. Exam: Model solutions. [181] W. Kahan. Complexity vs. cost. World- World-Wide Web document, March 18, Wide Web document, August 24, 1999. 1999. URL http://www.cs.berkeley. URL http://www.cs.berkeley.edu/~ edu/~wkahan/Math55/m55mr18s.pdf. wkahan/Math55/cmplxty.pdf. Lecture Lecture notes for Math 55. notes for Math 55. Kahan:1999:EMSd Kahan:1999:D [188] W. Kahan. Exam: Model solutions. [182] W. Kahan. Derangements. World- World-Wide Web document, May 11, Wide Web document, June 9, 1999. 1999. URL http://www.cs.berkeley. URL http://www.cs.berkeley.edu/~ edu/~wkahan/Math55/m55my11s.pdf. wkahan/Math55/derange.pdf. Lecture Lecture notes for Math 55. notes for Math 55. Kahan:1999:DTP Kahan:1999:EPI

[183] W. Kahan. Discussion of two prob- [189] W. Kahan. Enumerating pairs of in- lems in the text. World-Wide tegers. World-Wide Web document, Web document, February 3, 1999. April 30, 1999. URL http://www. URL http://www.cs.berkeley.edu/~ cs.berkeley.edu/~wkahan/Math55/ wkahan/Math55/m55jan28.pdf. Lec- pairs.pdf. Lecture notes for Math 55. ture notes for Math 55. Kahan:1999:FEM Kahan:1999:EGA [190] W. Kahan. Final exam: Model so- [184] W. Kahan. Euclid’s GCD algorithm. lutions. World-Wide Web document, World-Wide Web document, May 10, May 14, 1999. URL http://www. 1999. URL http://www.cs.berkeley. cs.berkeley.edu/~wkahan/Math55/ edu/~wkahan/Math55/gcd.pdf. Lec- m55finls.pdf. Lecture notes for Math ture notes for Math 55. 55. REFERENCES 26

Kahan:1999:FI Kahan:1999:OCT

[191] W. Kahan. The fragility of improb- [197] W. Kahan. Only commutators have ability. World-Wide Web document, trace zero. World-Wide Web docu- June 9, 1999. URL http://www. ment, June 10, 1999. URL http://www. cs.berkeley.edu/~wkahan/Math55/ cs.berkeley.edu/~wkahan/MathH110/ correln.pdf. Lecture notes for Math trace0.pdf. Lecture notes for Math 55. H110. Kahan:1999:FLT Kahan:1999:PS

[192] W. Kahan. Fermat’s little theo- [198] W. Kahan. Problems’ solutions. World- rem. World-Wide Web document, Wide Web document, December 15, March 1, 1999. URL http://www. 1999. URL http://www.cs.berkeley. cs.berkeley.edu/~wkahan/Math55/ edu/~wkahan/Math185/probsoln.pdf. fermat.pdf. Lecture notes for Math 55. Lecture notes for Math 185. Kahan:1999:RAI Kahan:1999:HP [199] W. Kahan. Rational approximations [193] W. Kahan. The halting problem. World- of irrationals. World-Wide Web docu- Wide Web document, March 13, 1999. ment, April 8, 1999. URL http://www. URL http://www.cs.berkeley.edu/~ cs.berkeley.edu/~wkahan/Math55/ wkahan/Math55/halting.pdf. Lecture p249n17.pdf. Lecture notes for Math notes for Math 55. 55. Kahan:1999:LLN Kahan:1999:SCD [194] W. Kahan. The Law of Large Numbers. [200] W. Kahan and Richard J. Fateman. World-Wide Web document, May 29, Symbolic computation of divided diﬀer- 1999. URL http://www.cs.berkeley. ences. SIGSAM Bulletin (ACM Spe- edu/~wkahan/Math55/largenos.pdf. cial Interest Group on Symbolic and Al- Lecture notes for Math 55. gebraic Manipulation), 33(2):7–28, June Kahan:1999:MS 1999. CODEN SIGSBZ. ISSN 0163-5824 (print), 1557-9492 (electronic). [195] W. Kahan. Math 55 syllabus. World- Kahan:1999:SFE Wide Web document, June 20, 1999. URL http://www.cs.berkeley.edu/~ [201] W. Kahan. Solutions for ﬁnal exam. wkahan/Math55/syllabus.pdf. Lec- World-Wide Web document, Decem- ture notes for Math 55. ber 11, 1999. URL http://www. Kahan:1999:MSS cs.berkeley.edu/~wkahan/Math185/ xm11decs.pdf. Lecture notes for Math [196] W. Kahan. Math 55 Spring 1999 syl- 185. labus. World-Wide Web document, Kahan:1999:SI May 6, 1999. URL http://www. cs.berkeley.edu/~wkahan/Math55/ [202] W. Kahan. Some inequalities. World- math55.pdf. Lecture notes for Math 55. Wide Web document, May 9, 1999. REFERENCES 27

URL http://www.cs.berkeley.edu/~ Kahan:1999:TMS wkahan/Math55/ineq.pdf. Lecture notes for Math 55. [208] W. Kahan. Test: Model solutions. World-Wide Web document, April 26, Kahan:1999:SP 1999. URL http://www.cs.berkeley. [203] W. Kahan. Solutions to problems. edu/~wkahan/Math55/m55ap26s.pdf. World-Wide Web document, Decem- Lecture notes for Math 55. ber 12, 1999. URL http://www. Kahan:1999:TPA cs.berkeley.edu/~wkahan/Math185/ 31aug99s.pdf. Lecture notes for Math [209] W. Kahan. Three problems about 185. combinatorial coeﬃcients. World- Wide Web document, April 26, 1999. Kahan:1999:SPH URL http://www.cs.berkeley.edu/~ [204] W. Kahan. Solutions to problems wkahan/Math55/ncr.pdf. Lecture notes in H. W. Lenstra’s notes. World- for Math 55. Wide Web document, July 9, 1999. Kahan:1999:WB URL http://www.cs.berkeley.edu/~ wkahan/Math55/lenstras.pdf. Lec- [210] W. Kahan. Waiting for a bus. World- ture notes for Math 55. Wide Web document, April 12, 1999. URL http://www.cs.berkeley.edu/~ Kahan:1999:SRD wkahan/Math55/bus.pdf. Lecture notes [205] W. Kahan. Square root without division. for Math 55. World-Wide Web document, Febru- Bhatia:2000:PNS ary 23, 1999. URL http://www.cs. berkeley.edu/~wkahan/ieee754status/[211] Rajendra Bhatia, William Kahan, and reciprt.pdf. Ren-Cang Li. Pinchings and norms of scaled triangular matrices. Technical Kahan:1999:SSE Report 2000-23, Department of Mathe- [206] W. Kahan. SOLVEzag: Solve the equa- matics, University of Kentucky, Lexing- tion z =(1− exp(−pz))/(pz) for z ≥ ton, KY, USA, 2000. URL http://www. 0 as a function of p ≥ 0. World- cs.uky.edu/~rcli/papers/kablrep. Wide Web document, August 1, 1999. ps. URL http://www.cs.berkeley.edu/ Bindel:2000:CGR ~wkahan/Math128/SOLVEzag.pdf; http://www.cs.berkeley.edu/~wkahan/[212] D. Bindel, J. Demmel, W. Kahan, Math128/SOLVEzag.ps. Lecture notes and O. Marques. On computing for Math 128. Givens rotations reliably and eﬃ- Kahan:1999:T ciently. LAPACK Working Note 148, Department of Computer Sci- [207] W. Kahan. Test. World-Wide ence, University of Tennessee, Knoxville, Web document, January 27, 1999. Knoxville, TN 37996, USA, October URL http://www.cs.berkeley.edu/~ 2000. URL http://www.netlib.org/ wkahan/Math55/jan27s.pdf. Lecture lapack/lawns/lawn148.ps; http: notes for Math 55. //www.netlib.org/lapack/lawnspdf/ REFERENCES 28

lawn148.pdf. UT-CS-00-449, October October 5, 2000. URL http://www. 2000. Published in [242]. cs.berkeley.edu/~wkahan/MathH110/ gcd5.pdf. Lecture notes for Math H110. He:2000:PAA Kahan:2000:GEO [213] Yun (Helen) He and Chris H. Q. Ding. Platforms: An accurate arith- [218] W. Kahan. Geometry of elementary metics approach. In ACM [327], page operations and subspaces: A contin- 150. ISBN 0-7803-9802-5. LCCN uation of notes titled “geometry of QA76.88 2000. URL http://csdl. elementary operations”. World-Wide computer.org/comp/proceedings/sc/ Web document, December 14, 2000. 2000/9802/00/9802toc.htm; http: URL http://www.cs.berkeley.edu/~ //www.sc2000.org/proceedings/info/ wkahan/MathH110/geos.pdf. Lecture fp.pdf. notes for Math H110. Kahan:2000:GMH Kahan:2000:AFE [219] W. Kahan. Grades for Math. H110. [214] W. Kahan. Answers for ﬁnal examina- World-Wide Web document, 2000. tion. World-Wide Web document, De- URL http://www.cs.berkeley.edu/~ cember 21, 2000. URL http://www. wkahan/MathH110/h110_00.pdf. Lec- cs.berkeley.edu/~wkahan/MathH110/ ture notes for Math H110. finals.pdf. Lecture notes for Math H110. Kahan:2000:HRQ Kahan:2000:AFV [220] W. Kahan. How to recognize a quadratic form. World-Wide Web document, Oc- [215] W. Kahan. Axioms for ﬁelds and vec- tober 31, 2000. URL http://www.cs. tor spaces. World-Wide Web docu- berkeley.edu/~wkahan/MathH110/qf. ment, May 17, 2000. URL http://www. pdf. Lecture notes for Math H110. cs.berkeley.edu/~wkahan/MathH110/ Axioms.pdf. Lecture notes for Math Kahan:2000:JNF H110. [221] W. Kahan. Jordan’s normal form. Kahan:2000:CPR World-Wide Web document, Decem- ber 7, 2000. URL http://www. [216] W. Kahan. Cross-products and rota- cs.berkeley.edu/~wkahan/MathH110/ tions in 2- and 3-dimensional Euclidean jordan.pdf. Lecture notes for Math spaces: Notes for math. H110. World- H110. Wide Web document, October 11, 2000. Kahan:2000:LAM URL http://www.cs.berkeley.edu/~ wkahan/Math128/Cross.pdf. Lecture [222] W. Kahan. Linear algebra and ma- notes for Math 128. trix theory. World-Wide Web docu- Kahan:2000:EGA ment, Fall 2000. URL http://www. cs.berkeley.edu/~wkahan/MathH110/ [217] W. Kahan. Euclid’s GCD algo- Topics.pdf. Lecture notes for Math rithm. World-Wide Web document, H110. REFERENCES 29

Kahan:2000:MAA URL http://www.cs.berkeley.edu/~ wkahan/MathH110/s10oct.pdf. Lec- [223] W. Kahan. Miscalculating area and an- ture notes for Math H110. gles of a needle-like triangle. World- Wide Web lecture notes for introductory Kahan:2000:PSb numerical analysis classes., March 24, 2000. URL http://www.cs.berkeley. [228] W. Kahan. Problems’ solutions. World- edu/~wkahan/Triangle.pdf. Wide Web document, November 27, 2000. URL http://www.cs.berkeley. Kahan:2000:MVM edu/~wkahan/MathH110/s21nov.pdf. Lecture notes for Math H110. [224] W. Kahan. Marketing versus mathematics and other ruminations on Kahan:2000:RDFa the design of floating-point arithmetic. Technical report, Mathemat- [229] W. Kahan. Ruminations on the ics Department and Electrical Engi- design of floating-point arithmetic. neering and Computer Science Depart- World-Wide Web document, April ment, University of California, Berke- 25, 2000. URL http://cs.nyu. ley, Berkeley, CA, USA, August 27, edu/cs/faculty/overton/book/docs/ 2000. 48 pp. URL http://www. KahanTalk.pdf. cs.berkeley.edu/~wkahan/MktgMath. pdf; http://www.cs.nyu.edu/cs/ Kahan:2000:RDFb faculty/overton/book/docs/KahanTalk. pdf. [230] W. Kahan. Marketing versus mathematics and other ruminations on Kahan:2000:NJI the design of floating-point arithmetic. Technical report, Mathemat- [225] W. Kahan. Notes on Jensen’s in- ics Department and Electrical Engi- equality for Math. H90. World-Wide neering and Computer Science Depart- Web document, September 27, 2000. ment, University of California, Berke- URL http://www.cs.berkeley.edu/~ ley, Berkeley, CA, USA, August 27, wkahan/MathH110/jensen.pdf. Lec- 2000. 48 pp. URL http://www.cs. ture notes for Math H110. berkeley.edu/%7Ewkahan/MktgMath. Kahan:2000:NVN pdf; http://www.cs.nyu.edu/cs/ faculty/overton/book/docs/KahanTalk. [226] W. Kahan. Notes on vector norms. pdf. World-Wide Web document, Decem- ber 6, 2000. URL http://www. Kahan:2000:TCE cs.berkeley.edu/~wkahan/MathH110/ normlite.pdf. Lecture notes for Math [231] W. Kahan. Topics covered for exam H110. purposes. World-Wide Web document, Kahan:2000:PSa December 12, 2000. URL http://www. cs.berkeley.edu/~wkahan/MathH110/ [227] W. Kahan. Problems’ solutions. World- covered.pdf. Lecture notes for Math Wide Web document, October 19, 2000. H110. REFERENCES 30

Li:2000:DIT URL http://www.cs.berkeley.edu/~ wkahan/BlaUboat.pdf. [232] X. S. Li, J. W. Demmel, D. H. Bai- ley, G. Henry, Y. Hida, J. Iskandar, Kahan:2001:MBR W. Kahan, A. Kapur, M. C. Martin, [236] W. Kahan. M. Brand’s 2nd re- T. Tung, and D. J. Yoo. Design, im- vised problem has infinitely many so- plementation and testing of extended lutions. World-Wide Web document, and mixed precision BLAS. LAPACK April 13, 2001. URL http://www. Working Note and University of Ten- cs.berkeley.edu/~wkahan/Math128/ nessee report 149 and CS-00-451, De- Brand2.pdf. Lecture notes for Math partment of Computer Science, Univer- 128. sity of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 2000. 61 Kahan:2001:NSF pp. URL http://www.netlib.org/ [237] W. Kahan. Names for standard- lapack/lawns/lawn149.ps; http: ized floating-point formats. Techni- //www.netlib.org/lapack/lawnspdf/ cal report, Mathematics Department lawn149.pdf. and Electrical Engineering and Com- Demmel:2001:CAF puter Science Department, Univer- sity of California, Berkeley, Berke- [233] J. Demmel, Ben Diament, W. Kahan, ley, CA, USA, May 17, 2001. 4 pp. Plamen Koev, Ming Gu, Stan Eisen- URL http://www.cs.berkeley.edu/~ stat, Ivan Slapniˇcar, Kresimir Veselić, wkahan/ieee754status/Names.pdf. and Zlatko Drmaˇc. The complexity of accurate floating point computation Kahan:2001:SFP and symbolic computing, or, can we [238] W. Kahan. SRTEST: A Fortran pro- do numerical linear algebra in poly- gram to test any SRT divider’s logic nomial time? Lecture slides, 2001. for quotient-digit selection. World- URL http://www.cs.berkeley.edu/~ Wide Web document, August 6, 2001. demmel/ISSAC2001_2.pdf. URL http://www.cs.berkeley.edu/~ Kahan:2001:ATA wkahan/srtest/. Kahan:2001:WDW [234] W. Kahan. Approximate trisection of an angle. World-Wide [239] W. Kahan. Why do we need a floating- Web document, January 31, 2001. point arithmetic standard? Technical URL http://www.cs.berkeley.edu/~ report, University of California, Berke- wkahan/trisect.pdf; http://www. ley, CA, USA, March 2001. 49 pp. cs.berkeley.edu/~wkahan/trisect. URL http://www.cs.berkeley.edu/ ps. ~wkahan/ieee754status/why-ieee. pdf. Kahan:2001:HBM Kahan:2001:WVT [235] W. Kahan. How blabber-mouth U-boats got sunk in World War II. World-Wide [240] W. Kahan. What has the volume Web document, November 24, 2001. of a tetrahedron to do with computer REFERENCES 31

programming languages? Techni- March 19, 2002. URL http://www. cal report, Department of Mathemat- cs.berkeley.edu/~wkahan/MathH110/ ics and Department of Electrical En- Adjx.pdf. Lecture notes for Math H110. gineering and Computer Science, Uni- versity of California, Berkeley, Berke- Kahan:2002:FPC ley, CA, USA, April 20, 2001. 31 pp. [246] W. Kahan. Fclass: a proposed clas- URL http://www.cs.berkeley.edu/~ sification of standard floating-point wkahan/VtetLang.pdf. operands. World-Wide Web docu- Bhatia:2002:PNS ment, March 23, 2002. URL http: //www.cs.berkeley.edu/%7Ewkahan/ [241] Rajendra Bhatia, William Kahan, and ieee754status/Fclass.pdf. Ren-Cang Li. Pinchings and norms of scaled triangular matrices. Linear Mul- Kahan:2002:HGI tilinear Algebra, 50(1):15–21, 2002. CO- DEN LNMLAZ. ISSN 0308-1087. [247] W. Kahan. Huge generalized inverses of rank-deficient matrices. World- Bindel:2002:CGR Wide Web document, May 2, 2002. [242] David Bindel, James Demmel, William URL http://www.cs.berkeley.edu/~ Kahan, and Osni Marques. On com- wkahan/MathH110/GIlite.pdf. Lec- puting Givens rotations reliably and ef- ture notes for Math H110. ficiently. ACM Transactions on Math- Kahan:2002:IBD ematical Software, 28(2):206–238, June 2002. CODEN ACMSCU. ISSN 0098- [248] W. Kahan. Idempotent binary → dec- 3500 (print), 1557-7295 (electronic). imal → binary conversion. World- Wide Web document, February 2, 2002. Kahan:2002:AI URL http://www.cs.berkeley.edu/~ [243] W. Kahan. About infinity. World- wkahan/Math128/BinDecBin.pdf. Lec- Wide Web document, March 7, 2002. ture notes for Math 128. URL http://www.cs.berkeley.edu/~ Kahan:2002:MFE wkahan/Infinity.pdf. [249] W. Kahan. Math. 110 final exam. Kahan:2002:ALN World-Wide Web document, May 27, [244] W. Kahan. Abbreviated lecture notes 2002. URL http://www.cs.berkeley. on ellipsoidal error bounds for trajectory edu/~wkahan/MathH110/Final02.pdf. calculations. World-Wide Web docu- Lecture notes for Math H110. ment, March 9, 2002. URL http://www. Kahan:2002:MIH cs.berkeley.edu/~wkahan/Math128/ Ellipsoi.pdf. Lecture notes for Math [250] W. Kahan. Matlab’s inverses of Hilbert 128. matrices. World-Wide Web document, Kahan:2002:CA May 2, 2002. URL http://www. cs.berkeley.edu/~wkahan/MathH110/ [245] W. Kahan. Computing an adju- HilbMats.pdf. Lecture notes for Math gate. World-Wide Web document, H110. REFERENCES 32

Kahan:2002:MPI http://www.cs.berkeley.edu/~wkahan/ Math128/RefinEig.pdf. Lecture notes [251] W. Kahan. Matlab programs for infor Math 128. Work in progress: not for terpolation and extrapolation. World- redistribution. Wide Web document, February 11, Kahan:2002:SCP 2002. URL http://www.cs.berkeley. edu/~wkahan/Math128/XPOLATE. Lec- [257] W. Kahan. Separation of clouds by ture notes for Math 128. a plane. World-Wide Web document, Kahan:2002:MTa May 17, 2002. URL http://www. cs.berkeley.edu/~wkahan/Math128/ [252] W. Kahan. Midterm test. World- Separate.pdf; http://www.cs.berkeley. Wide Web document, March 5, 2002. edu/~wkahan/MathH110/Separate.pdf. URL http://www.cs.berkeley.edu/~ Lecture notes for Math H110 and Math wkahan/MathH110/MidTerm.pdf. Lec- 128. ture notes for Math H110. Kahan:2002:TPM Kahan:2002:MTb [258] W. Kahan. Two problems: Must tri- [253] W. Kahan. Midterm test. World- angular matrices have triangular in- Wide Web document, April 29, 2002. verses? When are triangular fac- URL http://www.cs.berkeley.edu/~ torizations unique? World-Wide wkahan/MathH110/MidTerm2.pdf. Lec- Web document, February 20, 2002. ture notes for Math H110. URL http://www.cs.berkeley.edu/~ Kahan:2002:NAC wkahan/MathH110/TriFact.pdf. Lec- ture notes for Math H110. [254] W. Kahan. The numerical analyst as Kahan:2002:TRD computer science curmudgeon. World- Wide Web document, September 11, [259] W. Kahan. Thiele’s reciprocal dif- 2002. URL http://www.cs.berkeley. ferences and derivatives. World-Wide edu/~wkahan/Curmudge.pdf. Web document, February 14, 2002. Kahan:2002:ODE URL http://www.cs.berkeley.edu/~ wkahan/Math128/THIELEDF. Lecture [255] W. Kahan. An ordinary diﬀerential notes for Math 128. equation in interval-arithmetic. World- Li:2002:DIT Wide Web document, March 9, 2002. URL http://www.cs.berkeley.edu/~ [260] Xiaoye S. Li, James W. Demmel, wkahan/Math128/ODEintvl.pdf. Lec- David H. Bailey, Greg Henry, Yozo ture notes for Math 128. Hida, Jimmy Iskandar, William Kahan, Kahan:2002:RPR Suh Y. Kang, Anil Kapur, Michael C. Martin, Brandon J. Thompson, Teresa [256] W. Kahan. Refineig: a pro- Tung, and Daniel J. Yoo. Design, imple- gram to reﬁne eigensystems. World- mentation and testing of extended and Wide Web document, May 29, 2002. mixed precision BLAS. ACM Transac- URL http://www.cs.berkeley.edu/ tions on Mathematical Software, 28(2): ~wkahan/Math128/refineig.abs; 152–205, June 2002. CODEN ACMSCU. REFERENCES 33

ISSN 0098-3500 (print), 1557-7295 (elec- Kahan:2004:ASC tronic). [266] W. Kahan. Assignment: Solve A4z = Parlett:2002:QA b by conjugate gradient iteration without ever storing the matrix A . World- [261] Beresford N. Parlett. The QR algo- 4 Wide Web document, April 19, 2004. rithm. World-Wide Web document, URL http://www.cs.berkeley.edu/~ April 22, 2002. URL http://www. wkahan/Math128/a4d2.txt. Lecture cs.berkeley.edu/~wkahan/Math128/ notes for Math 128. Parlett.pdf. Lecture notes for Math 128. Kahan:2004:ASE

Shampine:2002:MOS [267] W. Kahan. Angle subtended at the [262] Lawrence F. Shampine and Mark W. Re- eye by neighboring stars. World-Wide ichelt. The Matlab ODE suite. World- Web document, September 17, 2004. Wide Web document, February 27, URL http://www.cs.berkeley.edu/~ 2002. URL http://www.cs.berkeley. wkahan/Math128/angle.pdf. Lecture edu/~wkahan/Math128/ODEsuite.pdf. notes for Math 128. Lecture notes for Math 128. Kahan:2004:CFP Kahan:2003:CPR [268] W. Kahan. On the cost of ﬂoating- [263] W. Kahan. Cross-products and rota- point computation without extra-precise tions in 2- and 3-dimensional Euclidean arithmetic. World-Wide Web document, spaces. World-Wide Web document, November 20, 2004. URL http://www. November 23, 2003. URL http://www. cs.berkeley.edu/~wkahan/Qdrtcs. cs.berkeley.edu/~wkahan/MathH110/ pdf. See [304] for a proof of this al- Cross.pdf. Lecture notes for Math gorithm for accurate computation of the H110. discriminant needed for the solution of quadratic equations. Randolph:2003:WKT Kahan:2004:DCP [264] Dan W. Randolph. William Kahan: 1989 Turing Award winner. Cosc [269] W. Kahan. Derivatives in the com- 5000 class report, Department of Com- plex z-plane. World-Wide Web docu- puter Science University of Wyoming, ment, May 26, 2004. URL http://www. Laramie, WY, USA, May 16, 2003. 7 cs.berkeley.edu/~wkahan/Math185/ pp. URL http://www.mapsharecorp. Derivative.pdf. Lecture notes for com/kahan.pdf. Math 185. Kahan:2004:A Kahan:2004:FMD

[265] W. Kahan. Abstracts. World-Wide [270] W. Kahan. Failure mode: Do MAT- Web document, November 1, 2004. LAB’s lu(...), inv(...), / and \ URL http://www.cs.berkeley.edu/~ have a failure mode? World-Wide wkahan/abstrcts. Abstracts of some of Web document, February 17, 2004. the online documents. URL http://www.cs.berkeley.edu/~ REFERENCES 34

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