A Bibliography of Publications of William M. Kahan fileA Bibliography of Publications of William M. Kahan Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155

A Bibliography of Publications of William M. Kahan

Nelson H. F. BeebeUniversity of Utah

Department of Mathematics, 110 LCB155 S 1400 E RM 233

Salt Lake City, UT 84112-0090USA

Tel: +1 801 581 5254FAX: +1 801 581 4148

E-mail: [email protected], [email protected],[email protected], [email protected] (Internet)

WWW URL: http://www.math.utah.edu/~beebe/

12 December 2019Version 1.69

Title word cross-reference

128 [276]. 2 [216, 263]. 2× 2 [306]. 3[216, 263]. A4 [266]. A4z = b [266]. f(x) = 0[57]. ∞/∞ [284]. M [67]. n× n [42]. p ≥ 0[206]. QR [32]. q×m− n [73]. → [248]. sin Θ[151].

√x [63]. x ∗ [1/x] < x/x = 1 [128]. xn

[177]. Z [42, 179, 269].z = (1− exp(−pz))/(pz) [206]. z ≥ 0 [206].‖Z − Z∗‖ ≤ ‖Z + Z∗‖(log2 n+ 0.038) [42].

-Dimensional [216, 263]. -matrices [67].-plane [179, 269].

1 [152]. 128B [277, 278]. 12th [314, 327].14th [322]. 15C [74]. 167 [4]. 168 [6]. 169[5]. 1971 [40]. 1975 [313, 312]. 1983 [318].1986 [320]. 1999 [196].

2-Dimensional [166]. 2007 [326]. 25th[321]. 2nd [236].

50th [326]. 52 [52]. 55 [195].

60 [31, 35]. 6600 [41]. 6600/7600 [41].

7094 [18, 22]. 7094-II [18, 22]. 754[133, 140, 309, 174]. 754r [288]. 75th [326].7600 [41]. 7th [319].

8087 [74]. ’83 [318].

Abbreviated [244]. Abstract [15].Abstracts [265]. Accuracy[93, 99, 106, 127, 296, 105, 150]. Accurate[102, 233, 213, 14, 290, 306]. Accurately[308]. ACM [323, 311, 176]. ACM/IEEE[323]. ACRITH [80]. Addition [13]. Adds[112]. Adjugate [245]. Ado [88].

1

2

Advantages [126]. Aitken [60]. Alan [176].Algebra [101, 233, 17, 107, 222, 87].ALGOL [35, 31, 35, 31]. Algorithm[304, 184, 217, 77, 261, 306, 124, 32, 4, 5, 6].Algorithms [43, 44, 45]. Almost[34, 94, 138]. Almost-Commuting [34].American [317]. Anadromic [294].Analyses [139, 160]. Analysis[152, 320, 18, 22, 37, 45, 111, 116, 122, 77,322, 306, 301, 27]. Analyst [254].Angewandte [315]. Angle [97, 234, 267].Angles [147, 223]. anniversary [326].Annual [311, 317, 314]. Anomalies [80].Answers [153, 214]. Any [57, 238].aphorisms [26]. Application [122].Applications [68, 305, 288, 149]. Applied[145, 307, 136]. Approach [213].Approximate [71, 234]. Approximation[164]. Approximations [199]. Apr. [40].April [320]. Area [97, 147, 223]. Argonne[313]. Arithmetic[78, 79, 56, 298, 319, 27, 29, 62, 66, 82, 83,90, 98, 100, 110, 131, 229, 239, 255, 268, 285,48, 64, 327, 309, 30, 72, 103, 104, 133, 140,142, 224, 230, 58, 75, 76, 146]. Arithmetics[213]. Arithmetik [48, 64]. arrival [326].Art [326, 320]. Assessments [271].Assignment [266]. assistant [295].Association [317]. Augmenting [110].August [311, 317, 310, 316]. Award[176, 264]. Axioms [167, 215].

Babuska [31, 35]. Babuska’sche [31, 35].Back [293]. Backward [6]. Baleful[145, 136]. Bases [172]. be [91, 104, 123].Beastly [137]. Before [309]. Benchmarks[127, 145, 136]. Beresford [303]. Besieged[285]. Bessel [20]. Better [103]. Between[316, 117]. Bidiagonal [93, 102]. Bilinear[164]. Binary[56, 58, 82, 95, 131, 146, 248, 114, 140].Birmingham [320]. birthday [326]. Bit[88]. Blabber [235]. Blabber-Mouth [235].blame [301]. BLAS [232, 260]. Boats [235].

Boston [311]. Boulder [316]. Bound[15, 21, 67]. Bounds[68, 282, 29, 71, 244, 297, 30, 28, 287, 20]. Br[315]. Branch [69, 88]. Brand [236]. Brief[283]. Bus [210]. Business [285].

Calculating [9, 97]. Calculation [4].Calculations [244]. Calculator[51, 57, 61, 55]. California [323, 318, 180].Can [233, 51, 55, 142, 292]. Canada[317, 314]. can’t [292]. Cantilever [148].cases [133]. Cayley [279, 289]. CDC [41].celebrating [326]. Center [325]. certain[133]. certification [290]. Challenges [107].Chapter [43]. \ [270]. Checking [89, 113].Chemistry [145, 136]. Chio [154]. Circle[24]. Circumscribing [25]. class [149].Classification [246]. Clean [100]. Cleve[309]. Clever [274]. Clouds [257].Clustered [134]. Clusters [23].Coefficients [154, 209]. Coins [178].Colorado [316]. Combinatorial [209].Commentary [29, 299]. Commutators[197]. Commuting [34]. Compensated[122]. Complete [27]. completely [52].Complex [69, 88, 110, 120, 179, 269].Complexity [233, 181]. Composition [144].Computable [15]. Computation [304, 233,138, 200, 268, 271, 293, 316, 306, 104].Computational [326, 106]. Computations[313, 139, 160]. computed [81]. Computer[314, 319, 29, 94, 127, 145, 240, 254, 327, 30,136]. Computer-Arithmetic [30].Computerized [107]. Computers[101, 41, 1, 124]. Computing[323, 324, 325, 212, 93, 233, 326, 308, 117,177, 245, 327, 317, 242, 299]. Concepts[99, 106, 105]. Concerning [29, 26].Condition [39]. Conference[311, 323, 322, 320, 316, 326, 318, 327].Confirming [113]. Confluence [39].Confluent [4]. Congress [310]. Conic[179]. Conjugate [266, 272]. Conserving[39]. Constant [135]. Constant-Round

3

[135]. constants [144]. Construct [135].Contains [24]. continuation [218].Continued [92]. Contracted [112].Contribution [65]. Convention [325].convergence [67, 32]. Conversation [150].Conversion [248, 114]. Corner [309].Correct [304]. Correcting [113].correction [124]. Correctly [95, 141, 89].Cost [181, 268]. Count [51, 55]. Course[27]. Covered [231]. Cray [321, 104]. CRC[299]. Cross [216, 263]. Cross-Products[216, 263]. CS [58]. Cubic [85]. Curbs [39].Curmudgeon [254]. Cuts [69, 88].

D. [44]. Dallas [325]. Dates [117].Davidson [308]. Davis [86, 151].Davis-Kahan [151].Davis-Kahan-Weinberger [86]. Day [117].DAYDATE [117]. Days [117]. Debate[298]. debug [292]. Dec [40]. Decimal[82, 248, 114]. Decisions [285]. Dedicated[303]. Deficient [247]. Defined [91].Definition [48, 64]. Degrades [148].Demonstration [284]. Derangements[182]. Derivative [161]. Derivatives[259, 269]. describe [103]. Design[229, 232, 260, 26, 224, 230]. Designers [72].Designing [108, 109, 115]. Determinant[161]. Determinants [125, 306].Developers [286]. Diagnostics [70].Diagonal [14, 155, 279, 19, 289].Differences [4, 5, 6, 200, 259]. different[52]. Differential[15, 255, 280, 21, 144, 149, 294]. difficult[133]. digit [238]. Digital [72]. dilation[86]. Dilations [68]. Dilemma [302].Dimensional [166, 216, 263]. Directions[326]. discrete [307]. Discriminant[304, 290]. Discussion [183, 32]. Divided[4, 5, 6, 200]. divider [238]. Division[132, 205, 89]. Do [66, 239, 270, 233, 240].done [104]. Double [12, 13].Double-Precision [12, 13]. Doubled [90].Doubled-Precision [90]. Down [125].

Draft [56]. Dual [172]. Duisburg [327].Dundee [322].

Echelon [168]. Editorial [303]. Effect[145, 136]. efficiently [212, 242].Eigenproblem [123]. Eigensystems[71, 256]. Eigenvalues [134, 14, 23].Eigenvectors [3, 8, 33]. electronic [1].Elementary [69, 88, 156, 218]. elements[19]. Elicited [173]. ellipse [46]. ellipsoid[25]. Ellipsoidal [244, 21]. ellipsoids [25].End [299]. Engineering [293, 27].Enumerating [189]. Environment [65].Environments [70]. Equation[57, 85, 255, 280, 1, 149, 206]. Equations[15, 154, 2, 21, 144, 149, 294]. Error[68, 282, 287, 15, 29, 37, 139, 160, 244, 280,297, 299, 30, 41, 21, 124]. Error-Bound[15]. Error-Bounds [297]. Errors [11]. etc[74, 117]. Euclid [184, 217]. Euclidean[216, 263]. Evaluates [61]. Evaluation [84].ever [266]. Every [42]. Everyone[158, 159]. Everywhere [158, 159]. exact[87]. Exam[185, 186, 187, 188, 190, 201, 231, 249].Examination [153, 214]. Exception [118].Exception-Handling [118]. Extended[232, 260]. Extension [101, 152, 143, 175].Extra [282, 268, 287]. Extra-Precise[268, 287]. Extrapolation [60, 251]. eye[267].

Factorizations [258]. Failure [270]. family[294]. far [49, 54]. Fclass [246]. Federation[310]. Fermat [192]. Few [308]. Fields[215]. Final [153, 190, 201, 214, 249].Finders [296]. Finding [162, 163, 273].Floating[78, 79, 56, 152, 233, 10, 59, 58, 62, 63, 66,75, 76, 82, 83, 90, 95, 118, 131, 146, 158, 159,229, 237, 239, 246, 268, 271, 285, 293, 309, 13,301, 173, 26, 89, 133, 140, 142, 224, 230, 295].Floating-Point [78, 10, 59, 63, 66, 75, 76,82, 83, 90, 95, 118, 131, 146, 158, 159, 229,

4

237, 239, 246, 268, 271, 285, 293, 173, 79,301, 89, 133, 140, 142, 224, 230, 295]. Form[168, 220, 221]. Formally [304]. Formats[237]. Forms [164]. Formula [161].Forsythe [326]. FORTRAN [7, 16, 238].Forward [5]. Four [26]. FPTRP [10].Fractions [92]. Fragility [191]. Francisco[318]. Freiburg [315]. function [206].Functions [69, 88, 20, 81]. Further[306, 143, 175, 11]. Futile [271]. Futility[98]. Future [326, 293].

Gain [165]. GAMM [327].GAMM-IMACS [327]. Gauss [2, 157].Gaussian [60]. GCD [184, 217]. Gene[326]. Genealogy [281]. Generalization[143, 175]. Generalized [247]. generating[20]. Geometry [156, 218]. George [326].German [55, 48, 64, 31, 35]. Germany[312, 315, 327]. Get [38]. Givens [212, 242].go [49, 54]. Golub [326, 307, 308]. Good[75, 76]. got [235]. Grades [219]. Gradient[266]. Gradients [272]. Gradual [283].Great [298]. Group [321]. Gu [275].Guaranteed [93]. Gustafson [299, 298].

H. [204]. H110 [216, 219]. H90 [225]. Half[274]. Halting [193]. Handheld [61].Handling [118]. hardware [26].Haugeland [44]. held [320, 315]. Help [38].Hermitian [23, 47]. High[323, 324, 325, 101, 93, 108, 109, 115].High-Performance [324, 101]. Higher [98].Higher-Precision [98]. Hilbert [250].Hirondo [40]. Home [170, 277]. Hough[44]. hour [142]. HP [74]. HP-15C [74].Huge [247]. Hurts [158, 159, 104].

IBM [80]. Idealized [148]. Idempotent[248]. IEEE [323, 58, 62, 63, 75, 76, 90, 131,133, 140, 146, 288, 309, 114, 174]. IEEE-CS[58]. IFIP [310, 316]. Ihre [48, 64]. Ihren[55]. II [8, 18, 22, 235]. III [33]. Ill[38, 39, 50, 307]. Ill-Condition [39].

Ill-Posed [38, 50, 307]. Illinois [319]. IMA[320]. IMA/SIAM [320]. IMACS [327].Implementation [43, 44, 48, 232, 64, 260].Implementierung [64, 48]. important[150]. Improbability [139, 160, 191].Improvement [77]. Improving [87].Inclusion [23]. independent [78, 79].Inequalities [202]. Inequality [225].Infinitely [236]. Infinity [243].Information [310]. Institut [315].Instruments [52]. Integer [154]. Integers[189]. Integrals [61, 87]. integrator [129].Intel [74]. interface [314]. International[310, 327, 315, 312]. Interpolation[5, 6, 251]. intersection [25]. Interval[27, 62, 255, 315, 312]. Interval-Arithmetic[255]. Interview [173, 174]. Introduction[72]. inv [270]. Inverse [9, 123]. Inverses[247, 250, 258]. Inversion [157]. Invited[29]. Irrationals [199]. irreducible [67].Iterate [272]. Iteration [119, 266].Iterative [282, 287]. IV [16].

Jacobi [161]. Java [324, 152, 158, 159].Jensen [225]. John [299, 298, 145]. Joint[320]. Jordan [157, 221]. Jose [323]. June[321, 322, 319].

K. [29]. Kahan[308, 48, 64, 86, 31, 35, 264, 175, 176, 281,304, 303, 134, 307, 298, 306, 53, 48, 64, 67,31, 35, 77, 129, 173, 174, 150, 151, 143].Kahan-Arithmetik [48, 64].Kahan-Babuska [31, 35].Kahan-Babuska’sche [31, 35]. Karlsruhe[312]. Keplerian [300]. Key [57].Knowledge [135]. Konnen [55]. Korteweg[149]. Kuki [40].

L [299]. Laboratory [313]. Laguerre[24, 119]. Lanczos [307, 45, 49, 54].Language [110]. Languages [145, 240, 316].LAPACK [101, 291]. Large [308, 194, 2].Last [304]. Law [194]. LCAS [111, 116].

5

learn [142]. Least [24, 164]. Least-Squares[164]. Lecture[27, 44, 131, 140, 145, 146, 162, 163, 244, 273].length [78, 79]. Lenstra [204]. Libraries[108, 109, 115, 291]. Library [101]. Like[97, 147, 223]. Linear[101, 233, 17, 154, 222, 2, 21]. Little [192].Ljubljana [310]. Local [280]. Logarithm[274]. logic [238]. Loss [165]. Lotfi [130].Lottery [180]. lu [270].

M [176]. M. [236]. Man [173]. Many [236].March [326]. Marketing [224, 230]. Math[216, 249, 277, 278, 195, 196]. Math.[219, 225]. Mathematics[326, 74, 145, 224, 230, 136, 312, 315, 281].Mathematik [315]. MATLAB[270, 165, 250, 251, 262]. Matrices[93, 102, 308, 305, 23, 34, 45, 71, 247, 250,258, 211, 241, 19, 47, 67]. Matrix[313, 9, 14, 42, 157, 222, 143, 175, 266, 294].Max [91]. May [312, 315, 314]. Meeting[321, 317]. memoriam [40]. Method[308, 24, 31, 35]. methods [307, 1, 2, 294].Michigan [27]. Micro [318, 318].MidTerm [252, 253]. might [104]. Min[91]. Mindless [271]. Ming [275]. Mini[318, 318]. Mini/Micro [318, 318].Minimizing [73]. Miscalculating[147, 223]. Mixed [232, 260]. Mode [270].Model [185, 186, 187, 188, 190, 208].Modes [288]. Moments [305].monotonicity [81]. Mortem [7]. Morton[281]. Mouth [235]. Much [88].Multiplication [95, 120]. Multiply [112].Multiply-Adds [112]. Must [258].

Names [237]. National [313]. Near [34, 70].nearly [47]. Need [66, 239]. Needle[97, 147, 223]. Needle-Like [97, 147, 223].neglect [19]. neighboring [267]. Network[324]. Networking [323, 325]. Neumann[145]. Newton [5, 6]. Next [291]. Nickel[29]. No [94, 138, 53]. Nobody [165].

Nonnormal [71]. nonsingular [67]. Norm[68, 86]. Norm-Preserving [68, 86].Normal [221]. Norms [226, 211, 241]. Note[20, 12, 175, 151]. Notes[27, 44, 119, 131, 146, 162, 166, 204, 216, 225,226, 244, 273, 140, 218]. Nothing [88].November [323, 325, 318]. NP [135].Numbers [121, 137, 194]. Numerical[108, 109, 115, 233, 326, 322, 320, 18, 17, 22,27, 70, 113, 139, 160, 254, 286, 316, 294, 150].Numerically [100]. Numerics [327].

Occasional [98]. ODE [262]. off [19].off-diagonal [19]. Old [173]. One [24, 142].Only [197]. Ontario [321, 314]. Open [286].Operands [246]. Operations [156, 218].Optimal [68]. Options [62]. Orbits [300].orders [144]. Ordinary[15, 255, 21, 144, 149]. organized [310].Orthogonality [70]. other [224, 230]. Our[106, 167]. Over/Underflow [10].Overrelaxation [272].

p754 [75, 76]. Package [80]. Pairs [189].Paper [29]. papers [317]. Paradoxes[99, 105, 106]. parallel [124]. Parlett [303].Part [130]. Performance[323, 324, 325, 101, 108, 109, 115]. Personal[57]. Perturbation [3, 8, 33, 28]. Physics[145, 136]. Pinchings [211, 241]. Pitfalls[50]. Plane [257, 179, 269]. Platforms [213].Point[78, 56, 152, 233, 10, 59, 58, 62, 63, 66, 75, 76,82, 83, 90, 95, 118, 131, 146, 158, 159, 229,237, 239, 246, 268, 271, 285, 293, 309, 13, 173,79, 26, 89, 133, 140, 142, 224, 230, 295, 301].Poisson [1]. Polynomial[233, 24, 84, 296, 297]. Portable[101, 108, 109, 115, 123]. Posed [38, 50, 307].Post [7, 327]. Post-Mortem [7].post-proceedings [327]. Pracniques [11].practical [32]. Precimonious [295].Precise [282, 268, 287]. Precision[90, 98, 232, 12, 13, 260, 295, 301].

6

prescribe [103]. presented [317, 318].Preserving [68, 86]. Press [299].Presubstitution [92, 284]. Probabilistic[139, 160]. Probability [96]. Problem[38, 36, 167, 169, 193, 198, 227, 228, 236, 46,53, 86]. Problems[50, 167, 171, 203, 204, 209, 258, 278, 307, 183].Procedure [7]. Proceedings[311, 323, 313, 321, 314, 319, 320, 316, 317,310, 322, 327, 312, 315]. process [49, 54].processing [310]. Products [216, 263].Prof. [275]. Program[65, 94, 256, 114, 238]. Programmer [123].Programming [65, 70, 110, 240, 316].programs [133, 251, 292]. Project [281].Prominence [155]. Proof [290, 135].Proposal [152]. Proposed[78, 79, 56, 59, 58, 62, 63, 75, 76, 246].Prospectus [101, 291]. Proven [304].Pseudo [9]. Pseudo-Inverse [9]. Purposes[231].

QDRTC [16]. QR [261]. Quadratic [220].Quadrature [305, 60]. Quasi [12, 13].Question [286]. quotient [238].quotient-digit [238].

Radix [78, 79]. Radix- [78, 79]. raising[144]. Rank [247]. Rank-Deficient [247].Rational [83, 199]. Real[42, 85, 162, 163, 273]. Rechner [55].Reciprocal [259]. Recognize [220]. record[318]. recurrence [20]. Reduced [168].Reducing [11]. reduction [307]. Refine[256]. Refineig [256]. Refinement[282, 287]. Refutation [111, 116].Relationship [316]. Relative [93]. reliably[212, 242]. Remarks [11]. Reminiscences[173]. Removable [100]. Residual [71].Revised [236]. Revision [152]. Riccati[294]. Robustness [65]. Root[162, 163, 205, 273]. Root-Finding[162, 163, 273]. Roots [276]. Rotation[3, 8, 33]. Rotations [216, 263, 212, 242].

Round [135]. Rounded [95, 141, 89].Rounding [288]. Roundoff[41, 84, 120, 148, 271]. Routine [10]. Row[168]. Row-Echelon [168]. Ruminations[224, 229, 230].

S [44]. S.O.R. [67]. San [323, 318]. Sand[74]. Satisfies [42]. SC2000 [325]. SC97[323, 323]. ScaLAPACK [291]. scaled[211, 241]. SCAN [327]. schemes [144, 149].Science [254, 293, 314]. Scientific[327, 104]. section [317]. Sections [179].Seidel [2]. selection [238]. Semantics[152, 70]. Semiannual [321]. Separation[257]. September [313, 327]. Series [280].sessions [318]. Set [167, 169]. Sharp [134].Should [91, 49, 54]. SIAM [320]. sich [55].Sign [88]. Significance [94, 138]. SIGSAM[53]. Simply [122]. Singular[93, 102, 308, 9]. Singularity [100]. Skew[279, 289]. Small [93, 289]. Software[63, 113, 286]. solution [53, 86]. Solutions[169, 170, 171, 185, 186, 187, 188, 190, 198,201, 203, 204, 208, 227, 228, 236]. Solve[57, 85, 206, 266]. Solver [280]. SOLVEzag[206]. solving [1, 2]. Some[28, 202, 81, 292]. something [52]. Space[167]. Spaces [166, 172, 215, 216, 263].Sparse [313, 308, 313]. Spectra [47].Spectrum [42]. Spring [196]. SQRT [141].Square [205, 276]. Squares [164, 276]. SR[52]. SR-52 [52]. SRT [132, 238]. SRTEST[238]. Stack [126]. Stamps [178]. Standard[78, 79, 56, 59, 58, 63, 66, 75, 76, 90, 140,146, 239, 246, 62, 131]. Standardized [237].Standards [174]. Stanford [326, 326].stars [267]. State [326, 320]. statistical[317]. statistics [314]. Status[131, 146, 140]. storing [266]. Study[143, 175]. subroutine [16]. Subspaces[218, 28]. subtended [267]. suitable [1].Suite [262, 133]. Summation[122, 31, 77, 35, 124]. Summer [27].Summierungsverfahren [31, 35]. Sunk

REFERENCES 7

[235]. Super [180]. Support [18, 22].Survey [37, 1]. Syllabus [195, 196].Symbolic [233, 107, 200, 87]. Symmetric[14, 45, 19]. symplectic [129]. Symposium[313, 319, 327, 315, 314, 312]. Syntax [70].System [18, 22]. Systems[135, 15, 107, 72, 87, 2, 21].

Take [170, 277]. Take-Home [170, 277].tanpi [302]. Taylor [280]. TC2 [316]. Test[95, 132, 141, 170, 171, 207, 208, 252, 253,277, 238]. Testing [113, 232, 114, 133, 260].Tests [296]. Tetrahedron [240]. Texas [52].text [183]. their [68]. Theorem[134, 192, 143, 175, 151]. Theorems [23].Theory [222, 96]. there [279, 289]. Thiele[259]. Three [209, 278]. Time [233]. titled[218]. Too [274]. Topics [231]. Toronto[317, 321]. Trace [197]. Trajectory [244].Transcription [298]. Transform [279, 289].Transparencies [275]. Trap [10]. Travails[123]. Tri [14, 19]. Tri-Diagonal [14, 19].Triangle [97, 147, 223]. Triangular[258, 211, 241]. Trick [154]. Tridiagonal[123]. Tripleo [64]. Triplets [308]. Triplex[31, 35, 31, 35]. Triplex-ALGOL[35, 31, 35, 31]. Trisection [234].Truncation [11]. Tuning [295, 301].Turing [176, 264]. Tutorial [283]. Twenty[107]. Two [258, 25, 183]. TX [325].

U [235]. U-Boats [235]. UCBTEST [133].Unconventional [149, 144, 129].Undebuggable [293]. Underflow [10, 283].Unique [168, 258]. Universitat [315].University [326, 314, 319, 320, 27]. Unum[298, 299]. upon [136, 145]. Urbana [319].USA [323, 325, 316]. User [321]. using[301].

V [176].Validated [327]. Validating [113]. Validat-ing/Testing/Confirming/Checking/Correcting[113]. Values [93, 102, 9]. Vector

[167, 172, 215, 226]. verlassen [55]. Version[134]. Versus [82, 127, 224, 230]. Visions[130]. Volume [240]. Vries [149]. vs[298, 181].

W [204]. W. [44, 129]. Waiting [210]. War[235]. Waterloo [314]. Week [117].Weinberger [86]. Well [38]. West[318, 312]. West-83 [318]. Whether[95, 89]. Which [24]. William[176, 281, 303, 298, 264, 173, 174, 150].Winner [264]. Without [205, 268, 266].Word [78, 79]. Word-length-independent[78, 79]. Working [316]. Workshop [324].World [235]. Would [123]. Would-be[123]. Written [74].

Yugoslavia [310].

Zero [135, 24, 197, 279, 296, 297, 289]. Zero-Finders [296]. Zero-Knowledge [135].

ReferencesKahan:1955:SMS

[1] William Morton Kahan. A survey ofmethods of solving Poisson’s equationsuitable for electronic computers. M.A.,University of Toronto, Toronto, ON,Canada, 1955. ii + 44 + 8 pp.

Kahan:1958:GSM

[2] William Morton Kahan. Gauss–Seidelmethods of solving large systems of lin-ear equations. Ph.D. thesis, Universityof Toronto, Toronto, ON, Canada, 1958.

Davis:1963:REP

[3] Chandler Davis. The rotation of eigen-vectors by a perturbation. I. Jour-nal of Mathematical Analysis and Ap-plications, 6:159–173, 1963. CODEN

REFERENCES 8

JMANAK. ISSN 0022-247x (print),1096-0813 (electronic). See [8, 33].

Kahan:1963:ACC

[4] W. Kahan and I. Farkas. Algorithm167: Calculation of confluent divideddifferences. Communications of theAssociation for Computing Machinery,6(4):164–165, April 1963. CODENCACMA2. ISSN 0001-0782 (print),1557-7317 (electronic).

Kahan:1963:ANIa

[5] W. Kahan and I. Farkas. Algorithm169: Newton interpolation with for-ward divided differences. Communica-tions of the Association for Comput-ing Machinery, 6(4):165, April 1963.CODEN CACMA2. ISSN 0001-0782(print), 1557-7317 (electronic).

Kahan:1963:ANIb

[6] W. Kahan and I. Farkas. Algorithm168: Newton interpolation with back-ward divided differences. Communica-tions of the Association for Comput-ing Machinery, 6(4):165, April 1963.CODEN CACMA2. ISSN 0001-0782(print), 1557-7317 (electronic).

Kahan:1964:FPM

[7] W. Kahan and J. J. Leppik. A FOR-TRAN post-mortem procedure. Com-munications of the Association for Com-puting Machinery, 7(1):15, January1964. CODEN CACMA2. ISSN 0001-0782 (print), 1557-7317 (electronic).

Davis:1965:REP

[8] Chandler Davis. The rotation of eigen-vectors by a perturbation. II. Jour-nal of Mathematical Analysis and Ap-plications, 11:20–27, 1965. CODEN

JMANAK. ISSN 0022-247x (print),1096-0813 (electronic). See [3, 33].

Golub:1965:CSV

[9] G. H. Golub and W. Kahan. Calcu-lating the singular values and pseudo-inverse of a matrix. Journal of the So-ciety for Industrial and Applied Mathe-matics: Series B, Numerical Analysis, 2(2):205–224, ???? 1965. ISSN 0887-459X(print), 1095-7170 (electronic).

Kahan:1965:FPO

[10] W. Kahan. The floating-point over/underflow trap routine FPTRP. InProgrammer’s Reference Manual. Insti-tute of Computer Science, Universityof Toronto, Toronto, Ontario, Canada,1965. LCCN ???? Section 4.1.

Kahan:1965:PFR

[11] W. Kahan. Pracniques: Further remarkson reducing truncation errors. Commu-nications of the Association for Comput-ing Machinery, 8(1):40, January 1965.CODEN CACMA2. ISSN 0001-0782(print), 1557-7317 (electronic).

Moller:1965:NQD

[12] Ole Møller. Note on quasi double-precision. Nordisk tidskrift for infor-mationsbehandling, 5(4):251–255, 1965.CODEN BITTEL, NBITAB. ISSN0006-3835 (print), 1572-9125 (elec-tronic). See [13].

Moller:1965:QDP

[13] Ole Møller. Quasi double-precision infloating point addition. Nordisk tidskriftfor informationsbehandling, 5(1):37–50,1965. CODEN BITTEL, NBITAB.ISSN 0006-3835 (print), 1572-9125 (elec-tronic). See also [12].

REFERENCES 9

Kahan:1966:AES

[14] W. Kahan. Accurate eigenvalues of asymmetric tri-diagonal matrix. Tech-nical Report CS41, Department ofComputer Science, Stanford University,Stanford, CA, USA, July 22, 1966. ????pp. Revised June 1968.

Kahan:1966:CEB

[15] W. M. Kahan. A computable error-bound for systems of ordinary differen-tial equations (abstract). SIAM Review,8:568–569, 1966. CODEN SIREAD.ISSN 0036-1445 (print), 1095-7200 (elec-tronic).

Kahan:1966:FIS

[16] W. Kahan. The FORTRAN IV subrou-tine QDRTC. Technical report, Com-puter library, McLennan Laboratories,University of Toronto, Toronto, ON,Canada, 1966.

Kahan:1966:NLA

[17] W. M. Kahan. Numerical linear algebra.Canadian mathematical bulletin = Bul-letin canadien de mathematiques, 9(??):757–801, ???? 1966. CODEN CMBUA3.ISSN 0008-4395 (print), 1496-4287 (elec-tronic).

Kahan:1966:ISS

[18] W. Kahan. 7094-II system support fornumerical analysis. SHARE SecretaryDistribution 159, C4537, December 12,1966.

Kahan:1966:WND

[19] W. Kahan. When to neglect off-diagonalelements of symmetric tri-diagonal ma-trices. Technical report CS42, Depart-ment of Computer Science, University of

California, Berkeley, CA, USA, July 25,1966. URL ftp://reports.stanford.

edu/pub/cstr/reports/cs/tr/66/42/

CS-TR-66-42.pdf.

Kahan:196x:ACM

[20] W. M. Kahan. Note on bounds for gen-erating Bessel functions by recurrence.196x.

Kahan:1967:EEB

[21] W. M. Kahan. An ellipsoidal errorbound for linear systems of ordinary dif-ferential equations. Report, ComputerScience, University of Toronto, Toronto,Canada, 1967. ???? pp.

Kahan:1967:ISS

[22] W. M. Kahan. 7094-II system sup-port for numerical analysis. In Proceed-ings of the 1967 Army Numerical Anal-ysis Conference (Wisconsin, May 1967),pages 175–208 + errata. U.S. Army Re-search Office, Research Triangle Park,NC, 1967. LCCN ???? ARO-D Report67-3. Reprint of [18].

Kahan:1967:ITC

[23] W. Kahan. Inclusion theorems for clus-ters of eigenvalues of Hermitian matri-ces. Report, Computer Science, Univer-sity of Toronto, Toronto, Canada, 1967.

Kahan:1967:LMC

[24] W. Kahan. Laguerre’s method and a cir-cle which contains at least one zero of apolynomial. SIAM Journal on Numer-ical Analysis, 4(3):474–482, September1967. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic).

REFERENCES 10

Kahan:1968:CEA

[25] W. M. Kahan. Circumscribing an ellip-soid about the intersection of two ellip-soids. Canadian mathematical bulletin =Bulletin canadien de mathematiques, 11(??):437–441, ???? 1968. CODEN CM-BUA3. ISSN 0008-4395 (print), 1496-4287 (electronic).

Kahan:1968:FAC

[26] W. Kahan. Four aphorisms concerningfloating point hardware design. ACMSIGNUM Newsletter, 3(2):??, July 1968.CODEN SNEWD6. ISSN 0163-5778(print), 1558-0237 (electronic).

Kahan:1968:MCI

[27] W. M. Kahan. A more complete inter-val arithmetic: Lecture notes for an En-gineering Summer Course in NumericalAnalysis at the University of Michigan.Technical report, University of Michi-gan, 1968.

Davis:1969:SNB

[28] Chandler Davis and W. M. Kahan. Somenew bounds on perturbation of sub-spaces. Bulletin of the American Math-ematical Society, 75(4):863–868, ????1969. CODEN BAMOAD. ISSN0002-9904 (print), 1936-881X (elec-tronic). URL http://projecteuclid.

org/euclid.bams/1183530664.

Kahan:1969:ICC

[29] W. M. Kahan. Invited commentary(concerning the invited paper of K.Nickel: Error bounds and computerarithmetic). In A. Morrell, editor, Proc.of IFIP Congress 1968, Vol. I, pages 60–62. North-Holland Publ. Comp., Ams-terdam, New York, Oxford, 1969.

Nickel:1969:EBC

[30] K. Nickel. Error bounds and computer-arithmetic. In A. J. H. Morrell, edi-tor, Proc. of IFIP-Congress 1968, Vol.I, pages 54–60. North-Holland Publ.Comp., Amsterdam, New York, Oxford,1969. Cf.: Kahan, W. M., Invited Com-mentary, Ibidem 60-62.

Nickel:1969:KBS

[31] K. Nickel. Das Kahan-Babuska’scheSummierungsverfahren In Triplex-Algol60. (German) [The Kahan-Babuskasummation method in Triplex-Algol 60].Interner Bericht Des Inst. F. Informatik69/3, Universitat Karlsruhe, Karlsruhe,Germany, 1969. Published in [35].

Parlett:1969:CPA

[32] B. N. Parlett and W. Kahan. On theconvergence of a practical QR algorithm.(With discussion). In Information Pro-cessing 68 (Proc. IFIP Congress, Edin-burgh, 1968), Vol. 1: Mathematics, Soft-ware, pages 114–118. North-Holland,Amsterdam, 1969.

Davis:1970:REP

[33] Chandler Davis and W. M. Kahan. Therotation of eigenvectors by a perturba-tion. III. SIAM Journal on NumericalAnalysis, 7(1):1–46, March 1970. CO-DEN SJNAAM. ISSN 0036-1429 (print),1095-7170 (electronic). See [3, 8].

Kahan:1970:ACM

[34] W. M. Kahan. Almost-commuting ma-trices are near commuting matrices.Manuscript, July 23, 1970.

Nickel:1970:KBS

[35] K. Nickel. Das Kahan-BabuskascheSummierungsverfahren in Triplex-AL-

REFERENCES 11

GOL 60. (German) [The Kahan-Babuska summation method in Triplex-ALGOL 60]. Zeitschrift fur AngewandteMathematik und Mechanik, 50:369–373,1970. CODEN ZAMMAX. ISSN 0044-2267 (print), 1521-4001 (electronic).

Kahan:1971:P

[36] W. Kahan. A problem. ACM SIGNUMNewsletter, 6(3):6, November 1971. CO-DEN SNEWD6. ISSN 0163-5778 (print),1558-0237 (electronic). See response[41].

Kahan:1971:SEA

[37] W. M. Kahan. A survey of error anal-ysis. In Freiman et al. [310], pages1214–1239. ISBN 0-7204-2063-6. LCCNQA76 .I575 1971. URL http://dblp.

uni-trier.de/db/conf/ifip/ifip71-

2.html#Kahan71. Eight booklets in twovolumes.

Anderson:1972:HHI

[38] Donald G. M. Anderson, Joseph Traub,and W. Kahan. How to help an ill-posedproblem get well. In ACM ’72 [311], page663. LCCN TK 7885 A84p 1972. Thefirst annual George Forsythe MemorialLecture, presented by W. Kahan.

Kahan:1972:CCC

[39] W. Kahan. Conserving confluence curbsill-condition. Technical Report 6, Com-puter Science Department, University ofCalifornia, Berkeley, August 1972. ????pp.

Kahan:1972:MHK

[40] W. Kahan. In memoriam: Hi-rondo Kuki: Apr. 25, 1925–Dec. 28,1971. ACM SIGNUM Newsletter, 7(1):8–10, April 1972. CODEN SNEWD6.

ISSN 0163-5778 (print), 1558-0237 (elec-tronic).

Dorr:1973:REC

[41] Fred W. Dorr and Cleve B. Moler.Roundoff error on the CDC 6600/7600computers. ACM SIGNUM Newslet-ter, 8(2):24–26, April 1973. CODENSNEWD6. ISSN 0163-5778 (print),1558-0237 (electronic). See [36] for theoriginal problem.

Kahan:1973:EMR

[42] W. Kahan. Every n × n matrix Zwith real spectrum satisfies ‖Z −Z∗‖ ≤‖Z + Z∗‖(log2 n + 0.038). Proceedingsof the American Mathematical Society,39:235–241, 1973. CODEN PAMYAR.ISSN 0002-9939 (print), 1088-6826 (elec-tronic).

Kahan:1973:IAC

[43] W. M. Kahan. Implementation of al-gorithms (chapter 12). Technical Re-port AD 769-124, National Technical In-formation Service, Springfield, Virginia,1973.

Kahan:1973:IAL

[44] W. Kahan. Implementation of algo-rithms (lecture notes by W. S. Hauge-land and D. Hough). Technical Re-port 20, Department of Computer Sci-ence, University of California, Berkeley,CA, USA, 1973. ???? pp.

Kahan:1974:ALA

[45] W. Kahan and B. N. Parlett. An anal-ysis of Lanczos algorithms for symmet-ric matrices. Technical Report ERL-M467, University of California, Berkeley,Berkeley, CA, USA, 1974.

REFERENCES 12

Kahan:1975:EP

[46] W. Kahan. An ellipse problem. SIGSAMBulletin (ACM Special Interest Groupon Symbolic and Algebraic Manipula-tion), 9(3):11–??, August 1975. CODENSIGSBZ. ISSN 0163-5824 (print), 1557-9492 (electronic).

Kahan:1975:SNH

[47] W. Kahan. Spectra of nearly Hermitianmatrices. Proceedings of the AmericanMathematical Society, 48:11–17, 1975.CODEN PAMYAR. ISSN 0002-9939(print), 1088-6826 (electronic).

Laveuve:1975:DKA

[48] S. E. Laveuve. Definition Einer Kahan-Arithmetik Und Ihre Implementierung.(German) [Definition of a Kahan arith-metic and its implementation]. In Nickel[312], pages 236–245. CODEN LNCSD9.ISBN 0-387-07170-9. ISSN 0302-9743 (print), 1611-3349 (electronic).LCCN QA297 .I541. DM30.00. URLhttp://link.springer-ny.com/link/

service/series/0558/tocs/t0029.

htm; http://www.springerlink.

com/content/978-0-387-07170-1;

http://www.springerlink.com/openurl.

asp?genre=issue&issn=0302-9743&

volume=29; https://link.springer.

com/book/10.1007/3-540-07170-9. Ger-man or English.

Kahan:1976:HFS

[49] W. Kahan and B. N. Parlett. How farshould you go with the Lanczos process?In Bunch and Rose [313], pages 131–144. ISBN 0-12-141050-1. LCCN QA188.S989 1975.

Kahan:1976:PIP

[50] W. M. Kahan. Pitfalls in ill-posed prob-lems. SIAM Review, 18(4):810–811, ????1976. CODEN SIREAD. ISSN 0036-1445 (print), 1095-7200 (electronic).

Kahan:1977:CYC

[51] W. M. Kahan and B. N. Parlett. Canyou count on your calculator? Memo-randum UCB/ERL M77/21, ElectronicsResearch Laboratory, College of Engi-neering, University of California, Berke-ley, Berkeley, CA, USA, April 6, 1977. ii+ 28 pp. URL http://www.math.utah.

edu/pub/bibnet/authors/k/kahan-

william-m.bib; http://www.math.

utah.edu/pub/bibnet/subjects/acc-

stab-num-alg.bib. German Transl.Published In: Jahrbuch UberblickeMathematik 1978, Ed. by B. Fuchssteinerand others, Bibliographisches Institut,Mannheim-Wien-Zurich, 199–216, 1978.

Kahan:1977:NSC

[52] W. Kahan. And now for something com-pletely different: The Texas InstrumentsSR-52. Memorandum No. UCB/ERLM77/23, Electronics Research Labora-tory, College of Engineering, Universityof California, Berkeley, April 1977. ????pp.

Lauer:1977:SKP

[53] Markus Lauer. A solution to Ka-han’s problem (SIGSAM problem no.9). SIGSAM Bulletin (ACM SpecialInterest Group on Symbolic and Alge-braic Manipulation), 11(2):16–20, ????1977. CODEN SIGSBZ. ISSN 0163-5824(print), 1557-9492 (electronic).

REFERENCES 13

Kahan:1978:HFS

[54] W. Kahan and B. N. Parlett. How farshould you go with the Lanczos process?Memorandum UCB/ERL M78/48, Elec-tronics Research Laboratory, College ofEngineering, University of California,Berkeley, Berkeley, CA, USA, 1978. 16pp.

Kahan:1978:KSI

[55] W. Kahan and B. N. Parlett. Konnen Siesich auf Ihren Rechner verlassen? (Ger-man) [can you count on your calcula-tor?]. Jahrbuch Uberblicke Mathematik,??:199–216, 1978.

Coonen:1979:PSB

[56] Jerome Coonen, William Kahan, JohnPalmer, Tom Pittman, and DavidStevenson. A proposed standard for bi-nary floating point arithmetic: Draft5.11. ACM SIGNUM Newsletter, 14(3S (Special issue)):4–12, October 1979.CODEN SNEWD6. ISSN 0163-5778(print), 1558-0237 (electronic).

Kahan:1979:PCK

[57] William M. Kahan. Personal calcu-lator has key to solve any equationf(x) = 0. Hewlett-Packard Jour-nal: technical information from thelaboratories of Hewlett-Packard Com-pany, 30(12):20–26, December 1979.CODEN HPJOAX. ISSN 0018-1153.URL http://www.cs.berkeley.edu/~

wkahan/Math128/SOLVEkey.pdf. Lec-ture notes for Math 128.

Kahan:1979:PIC

[58] W. Kahan, J. Palmer, and J. Coo-nen. Proposed IEEE-CS Standard forBinary Floating Point Arithmetic. In

Gentleman [314], pages 32–36. LCCNQA276.4.

Kahan:1979:PFP

[59] W. Kahan and J. Palmer. On a proposedfloating-point standard. ACM SIGNUMNewsletter, 14(3S (Special issue)):13–21, October 1979. CODEN SNEWD6.ISSN 0163-5778 (print), 1558-0237 (elec-tronic).

Kahan:1980:AEG

[60] W. Kahan. Aitken’s extrapolation andGaussian quadrature. IEEE Floating-Point Subcommittee Working Docu-ment P754/80-1.19, 1980.

Kahan:1980:HCE

[61] William M. Kahan. Handheld cal-culator evaluates integrals. Hewlett-Packard Journal: technical informationfrom the laboratories of Hewlett-PackardCompany, 31(8):23–32, August 1980.CODEN HPJOAX. ISSN 0018-1153.URL http://www.cs.berkeley.edu/~

wkahan/Math128/INTGTkey.pdf. Lec-ture notes for Math 128.

Kahan:1980:IAO

[62] William M. Kahan. Interval arithmeticoptions in the proposed IEEE FloatingPoint Arithmetic Standard. In Nickel[315], pages 99–128. ISBN 0-12-518850-1. LCCN QA297.75 .I57 1980.

Kahan:1980:SPI

[63] W. Kahan. Software√x for the

proposed IEEE floating-point standard.Manuscript, August 25, 1980.

Laveuve:1980:DKA

[64] S. E. Laveuve. Definition Einer Kahan-Arithmetik Und Ihre Implementierung

REFERENCES 14

In Tripleo. (German) [Definition of aKahan Arithmetic and its implementa-tion in Tripleo]. Academic Press, NewYork, NY, USA, 1980. 355–366 pp.

Kahan:1981:PEC

[65] W. Kahan. The programming envi-ronment’s contribution to program ro-bustness. ACM SIGNUM Newsletter,16(4):10–??, October 1981. CODENSNEWD6. ISSN 0163-5778 (print),1558-0237 (electronic).

Kahan:1981:WDW

[66] W. Kahan. Why do we need a floating-point arithmetic standard? Technicalreport, University of California, Berke-ley, CA, USA, February 12, 1981. 41pp.

Neumann:1981:KRC

[67] M. Neumann. The Kahan S.O.R. con-vergence bound for nonsingular and ir-reducible M -matrices. Linear Algebraand its Applications, 39:205–222, 1981.CODEN LAAPAW. ISSN 0024-3795(print), 1873-1856 (electronic).

Davis:1982:NPD

[68] Chandler Davis, W. M. Kahan, andH. F. Weinberger. Norm-preserving di-lations and their applications to optimalerror bounds. SIAM Journal on Nu-merical Analysis, 19(3):445–469, June1982. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic). See[86].

Kahan:1982:BCC

[69] W. Kahan. Branch cuts for complex el-ementary functions. Technical ReportPAM-105, Center for Pure and Applied

Mathematics, University of California,Berkeley, CA, USA, October 1982.

Kahan:1982:NOS

[70] W. Kahan and Jerome T. Coonen. Thenear orthogonality of syntax, semantics,and diagnostics in numerical program-ming environments. In Reid [316], pages103–115. ISBN 0-444-86377-X. LCCNQA297 .I34 1981.

Kahan:1982:RBA

[71] W. Kahan, B. N. Parlett, and E. Jiang.Residual bounds on approximate eigen-systems of nonnormal matrices. SIAMJournal on Numerical Analysis, 19(3):470–484, June 1982. CODEN SJNAAM.ISSN 0036-1429 (print), 1095-7170 (elec-tronic).

Waser:1982:IAD

[72] Shlomo Waser and Michael J. Flynn. In-troduction to Arithmetic for Digital Sys-tems Designers. Holt, Rinehart andWinston, New York, 1982. ISBN 0-03-060571-7. xvii + 308 pp. LCCNTK7895.A65 W37 1982.

Kahan:1983:M

[73] W. Kahan. Minimizing q × m −n. Technical report, Department ofMathematics and Department of Elec-trical Engineering and Computer Sci-ence, University of California, Berke-ley, Berkeley, CA, USA, March 1983.URL http://www.cs.berkeley.edu/~

wkahan/testpi/nearpi.c.

Kahan:1983:MWS

[74] W. Kahan. Mathematics written insand — the HP-15C, Intel 8087, etc.In Anonymous [317], pages 12–26.ISBN ???? ISSN 0149-9963. LCCN

REFERENCES 15

QA276.4 .A43a. URL http://www.

cs.berkeley.edu/~wkahan/MathSand.

pdf.

Kahan:1983:PISa

[75] W. Kahan. The proposed IEEE Stan-dard p754 for Floating-Point Arith-metic: What good is it? Manuscript,1983.

Kahan:1983:PISb

[76] W. Kahan. The proposed IEEE Stan-dard p754 for Floating-Point Arith-metic: What good is it? In IEEE [318],page ??

Ozawa:1983:AIK

[77] K. Ozawa. Analysis and improvement ofKahan’s summation algorithm. Journalof Information Processing (of Japan??),6(4):226–230, 1983.

Cody:1984:PRW

[78] William J. Cody, Jr., Jerome T.Coonen, David M. Gay, K. Hanson,David Hough, W. Kahan, R. Karpin-ski, John F. Palmer, F. N. Ris, andD. Stevenson. A proposed radix- andword-length-independent standard forfloating-point arithmetic. IEEE Micro, 4(4):86–100, July/August 1984. CODENIEMIDZ. ISSN 0272-1732 (print), 1937-4143 (electronic).

Cody:1985:PRW

[79] W. J. Cody, J. T. Coonen, D. M.Gay, K. Hanson, D. Hough, W. Ka-han, R. Karpinski, J. Palmer, F. N. Ris,and D. Stevenson. A proposed radix-and word-length-independent standardfor floating-point arithmetic. ACMSIGNUM Newsletter, 20(1):37–51, Jan-uary 1985. CODEN SNEWD6. ISSN

0163-5778 (print), 1558-0237 (elec-tronic).

Kahan:1985:AIA

[80] W. Kahan and E. LeBlanc. Anoma-lies in the IBM ACRITH pack-age. In Hwang [319], pages 322–331. ISBN 0-8186-0632-0 (paper-back), 0-8186-8632-4 (hard), 0-8186-4632-2 (microfiche). LCCN QA76.9.C62S95 1985. URL http://www.acsel-

lab.com/arithmetic/arith7/papers/

ARITH7_Kahan_LeBlanc.pdf.

Kahan:1985:MSC

[81] W. Kahan. On the monotonicity of somecomputed functions. Technical ReportPAM-261, Center for Pure and AppliedMathematics, University of California,Berkeley, CA, USA, January 1985.

Kahan:1986:DVB

[82] W. Kahan. Decimal versus binaryfloating-point arithmetic. Manuscript,November 12, 1986.

Kahan:1986:RAF

[83] W. Kahan. Rational arithmetic infloating-point. Technical Report PAM-343, Center for Pure and Applied Math-ematics, University of California, Berke-ley, CA, USA, September 1986. 8 pp.

Kahan:1986:RPE

[84] W. Kahan. Roundoff in polynomial eval-uation. Manuscript, November 16, 1986.

Kahan:1986:SRC

[85] W. Kahan. To solve a real cubicequation. Technical Report PAM-352,Center for Pure and Applied Mathe-matics, University of California, Berke-ley, CA, USA, November 1986. 20

REFERENCES 16

pp. URL http://www.eecs.berkeley.

edu/~wkahan/Math128/Cubic.pdf.

Meinguet:1986:DKW

[86] Jean Meinguet. On the Davis-Kahan-Weinberger solution of the norm-preserving dilation problem. Nu-merische Mathematik, 49(2/3):331–341,July 1986. CODEN NUMMA7. ISSN0029-599X (print), 0945-3245 (elec-tronic). Refers to the work [68].

Fateman:1987:IEI

[87] Richard J. Fateman and W. Kahan.Improving exact integrals from sym-bolic algebra systems. Technical Re-port PAM-261, Center for Pure and Ap-plied Mathematics, University of Cal-ifornia, Berkeley, CA, USA, August1987. URL http://www.cybertester.

com/data/iintegr.pdf.

Kahan:1987:BCC

[88] W. Kahan. Branch cuts for complex el-ementary functions or much ado aboutnothing’s sign bit. In Iserles and Pow-ell [320], pages 165–211. ISBN 0-19-853614-3. LCCN QA297.J65 1986. URLhttp://people.freebsd.org/~das/

kahan86branch.pdf; http://www.

cs.berkeley.edu/~dbindel/class/

cs279/.

Kahan:1987:CWF

[89] W. Kahan. Checking whether floating-point division is correctly rounded. Lec-ture notes., 1987.

Kahan:1987:DPI

[90] W. Kahan. Doubled-precision IEEEstandard 754 floating-point arithmetic.Manuscript, February 26, 1987.

Kahan:1987:HSM

[91] W. Kahan. How should Max and Min bedefined? Manuscript, August 19, 1987.

Kahan:1987:PCF

[92] W. Kahan. Presubstitution and contin-ued fractions. Manuscript, March 17,1987.

Demmel:1988:CSS

[93] J. Demmel and W. Kahan. Com-puting small singular values of bidi-agonal matrices with guaranteed highrelative accuracy. LAPACK WorkingNote 03, Mathematics and ComputerScience Division, Argonne National Lab-oratory, 9700 South Cass Avenue, Ar-gonne, IL 60439-4801, USA, February1988. URL http://www.netlib.org/

lapack/lawns/lawn03.ps; http:/

/www.netlib.org/lapack/lawnspdf/

lawn03.pdf. ANL, MCS-TM-110,February 1988.

Kahan:1988:CPA

[94] W. Kahan. A computer program withalmost no significance. Manuscript,November 9, 1988.

Kahan:1988:TWB

[95] W. Kahan. To test whether binaryfloating-point multiplication is correctlyrounded. Manuscript, July 1988.

Lenstra:1988:PT

[96] H. W. Lenstra, Jr. Probability the-ory. World-Wide Web document,November 1988. URL http://www.

cs.berkeley.edu/~wkahan/Math55/

Lenstra.pdf. Lecture notes for Math55.

REFERENCES 17

Kahan:1989:CAA

[97] W. Kahan. Calculating area and angle ofa needle-like triangle. Manuscript, Jan-uary 26, 1989.

Kahan:1989:OFH

[98] W. Kahan. The occasional futility ofhigher-precision arithmetic. Manuscript,September 28, 1989.

Kahan:1989:PCA

[99] W. Kahan. Paradoxes in concepts of ac-curacy. Lecture notes from Joint Semi-nar on Issues and Directions in ScientificComputation, Berkeley, 1989.

Kahan:1989:SRN

[100] W. Kahan. A singularity removablenumerically when arithmetic is clean.Manuscript, May 17, 1989.

Anderson:1990:PEL

[101] E. Anderson, C. Bischof, J. Demmel,J. Dongarra, J. Du Croz, S. Hammar-ling, and W. Kahan. Prospectus for anextension to LAPACK: A portable lin-ear algebra library for high-performancecomputers. LAPACK Working Noteand Computer Science Dept. Techni-cal Report 26 and CS-90-118, Depart-ment of Computer Science, Univer-sity of Tennessee, Knoxville, Knoxville,TN 37996, USA, November 1990. 10pp. URL http://www.netlib.org/

lapack/lawns/lawn26.ps; http:/

/www.netlib.org/lapack/lawnspdf/

lawn26.pdf. LAPACK Working Note#26. UT-CS-90-118, November 1990.

Demmel:1990:ASV

[102] James W. Demmel and W. Kahan. Ac-curate singular values of bidiagonal ma-trices. SIAM Journal on Scientific

and Statistical Computing, 11(5):873–912, September 1990. CODEN SIJCD4.ISSN 0196-5204.

Kahan:1990:BPA

[103] W. Kahan. Better to prescribe arith-metic than describe it. Technical re-port, Department of Computer Science,University of California, Berkeley, CA,USA, February 21, 1990. Turing AwardLecture presented at ACM Conference,Washington.

Kahan:1990:HCA

[104] W. Kahan. How Cray’s arithmetichurts scientific computation (and whatmight be done about it). In CUG [321],page 42. ISBN ???? LCCN ???? URLhttp://754r.ucbtest.org/issues/

cray-hurts-uk.pdf; http://754r.

ucbtest.org/issues/cray-hurts-ut.

pdf; http://754r.ucbtest.org/

issues/cray-hurts.pdf. Manuscriptprepared for the Cray User Group meet-ing in Toronto, Canada, April 10, 1990.

Kahan:1990:PCA

[105] William Kahan. Paradoxes in conceptsof accuracy, 1990. 1 videocassette (60min.).

Kahan:1990:POC

[106] W. Kahan. Paradoxes in our conceptsof computational accuracy. Manuscript,October 1, 1990.

Kahan:1990:TCC

[107] W. Kahan. Twenty challenges forcomputerized symbolic algebra systems.Manuscript, August 16, 1990.

Demmel:1991:DPHa

[108] James Demmel, Jack Dongarra, andW. Kahan. On designing portable high

REFERENCES 18

performance numerical libraries. LA-PACK Working Note 39, Departmentof Computer Science, University of Ten-nessee, Knoxville, Knoxville, TN 37996,USA, July 1991. URL http://www.

netlib.org/lapack/lawns/lawn39.

ps; http://www.netlib.org/lapack/

lawnspdf/lawn39.pdf. UT-CS-91-141,July, 1991.

Demmel:1991:DPHb

[109] J. Demmel, J. Dongarra, and W. Ka-han. On designing portable high perfor-mance numerical libraries. In Griffithsand Watson [322], page ?? ISBN 0-582-08908-5. LCCN QA297 .D85 1991.

Kahan:1991:APL

[110] William Kahan and J. W. Thomas. Aug-menting a programming language withcomplex arithmetic. Technical ReportNCEG/91-039, UCB/CSD 91/667, De-partment of Computer Science, Univer-sity of California, Berkeley, CA, USA,November 15, 1991. 8 pp. Manuscript.

Kahan:1991:ARL

[111] W. Kahan. Analysis and refutation ofthe LCAS. ACM SIGNUM Newslet-ter, 26(3):2–15, July 1991. CODENSNEWD6. ISSN 0163-5778 (print),1558-0237 (electronic).

Kahan:1991:CMA

[112] W. Kahan. Contracted multiply-adds.Manuscript, September 20, 1991.

Kahan:1991:VTC

[113] W. Kahan. Validating/testing/confirming/checking/correcting numeri-cal software. Manuscript, November 26,1991.

Paxson:1991:PTI

[114] Vern Paxson and W. Kahan. A pro-gram for testing IEEE binary–decimalconversion. World-Wide Web document,May 1991. URL ftp://ftp.ee.lbl.

gov/testbase-report.ps.Z; ftp:/

/ftp.ee.lbl.gov/testbase.tar.Z.

Demmel:1992:DPH

[115] James W. Demmel, J. J. Dongarra,and W. Kahan. On designing portablehigh performance numerical libraries. InD. F. Griffiths and G. A. Watson, ed-itors, Numerical Analysis 1991, Pro-ceedings of the 14th Dundee Conference,volume 260 of Pitman Research Notesin Mathematics, pages 69–84. LongmanScientific and Technical, Harlow, Essex,UK, 1992.

Kahan:1992:ARL

[116] W. Kahan. Analysis and refutation ofthe LCAS. ACM SIGPLAN Notices, 27(1):61–74, January 1992. CODEN SIN-ODQ. ISSN 0362-1340 (print), 1523-2867 (print), 1558-1160 (electronic).

Kahan:1992:DCD

[117] W. Kahan. DAYDATE: Computingdays between dates, the day of theweek, etc. World-Wide Web document,September 16, 1992. URL http://www.

cs.berkeley.edu/~wkahan/daydate/.

Kahan:1992:FPE

[118] W. Kahan. Floating-point exception-handling. Manuscript, July 31, 1992.

Kahan:1992:NLI

[119] W. Kahan. Notes on Laguerre’s itera-tion. Manuscript, December 4, 1992.

REFERENCES 19

Kahan:1992:RCM

[120] W. Kahan. Roundoff in complex mul-tiplication. Manuscript, November 11,1992.

Kahan:1992:WN

[121] W. Kahan. What numbers? Manu-script, September 9, 1992.

Kahan:1993:AAS

[122] W. Kahan. Analysis and application ofsimply compensated summation. Manu-script, September 7, 1993.

Kahan:1993:TIE

[123] W. Kahan. A tridiagonal inverse eigen-problem and the travails of a would-beportable programmer. Manuscript, June1, 1993.

Ozawa:1993:SAE

[124] K. Ozawa and M. Miyazaki. A sum-mation algorithm with error correctionfor parallel computers. Systems andComputers in Japan, 24(7):62–68, ????1993. CODEN SCJAEP. ISSN 0882-1666 (print), 1520-684X (electronic). See[11].

Axler:1994:DD

[125] Sheldon Axler. Down with determi-nants! World-Wide Web document,December 21, 1994. URL http://www.

cs.berkeley.edu/~wkahan/MathH110/

DownDets.pdf. Lecture notes for MathH110.

Kahan:1994:AS

[126] W. Kahan. On the advantages of the8087’s stack. Manuscript, August 23,1994.

Kahan:1994:CBV

[127] W. Kahan. Computer benchmarks ver-sus accuracy. Draft manuscript, June1994.

Kahan:1994:W

[128] W. Kahan. When is x∗[1/x] < x/x = 1?Manuscript, January 1, 1994.

Sanz-Serna:1994:USI

[129] J. M. Sanz-Serna. An unconventionalsymplectic integrator of W. Kahan. Ap-plied Numerical Mathematics: Transac-tions of IMACS, 16(1–2):245–250, De-cember 1, 1994. CODEN ANMAEL.ISSN 0168-9274 (print), 1873-5460 (elec-tronic). URL http://www.elsevier.

com/cgi-bin/cas/tree/store/apnum/

cas_sub/browse/browse.cgi?year=

1994&volume=16&issue=1-2&aid=506.A Festschrift to honor Professor RobertVichnevetsky on his 65th birthday.

Woehr:1994:LVP

[130] Jack Woehr. Lotfi visions, part 2. Dr.Dobb’s Journal of Software Tools, 19(8):52–??, August 1994. CODEN DDJOEB.ISSN 1044-789X.

Kahan:1995:LNS

[131] W. Kahan. Lecture notes on the sta-tus of IEEE Standard 754 for binaryfloating-point arithmetic. Manuscript,May 23, 1995.

Kahan:1995:TSD

[132] W. Kahan. A test for SRT division. Lec-ture notes, 1995. URL http://www.cs.

berkeley.edu/~wkahan/srtest.

Kahan:1995:USP

[133] Students of Prof. W. Kahan. UCB-TEST: a suite of programs for test-

REFERENCES 20

ing certain difficult cases of IEEE 754floating-point arithmetic. World-WideWeb document, March 12, 1995. URLhttp://www.netlib.org/fp/ucbtest.

tgz.

Cao:1996:SVK

[134] Zhi hao Cao, Jin jun Xie, and Ren-Cang Li. A sharp version of Ka-han’s theorem on clustered eigenval-ues. Linear Algebra and its Ap-plications, 245(1–3):147–155, Septem-ber 15, 1996. CODEN LAAPAW.ISSN 0024-3795 (print), 1873-1856 (elec-tronic). URL http://www.elsevier.

com/cgi-bin/cas/tree/store/laa/


1996&volume=245&issue=1-3&aid=9400226.

Goldreich:1996:HCC

[135] Oded Goldreich and Ariel Kahan.How to construct constant-round zero-knowledge proof systems for NP. Jour-nal of Cryptology: the journal of theInternational Association for Crypto-logic Research, 9(3):167–189, Summer1996. CODEN JOCREQ. ISSN0933-2790 (print), 1432-1378 (elec-tronic). URL http://link.springer.

de/link/service/journals/00145/

bibs/9n3p167.html; http://link.

springer.de/link/service/journals/

00145/bibs/9n3p167.pdf; http:/

/link.springer.de/link/service/

journals/00145/bibs/9n3p167.tex;

http://link.springer.de/link/service/

journals/00145/tocs/00903.html.

Kahan:1996:BEC

[136] W. Kahan. The baleful effect ofcomputer benchmarks upon appliedmathematics, physics, and chemistry.World-Wide Web document., 1996.

URL http://www.cs.berkeley.edu/~

wkahan/ieee754status/baleful.ps.

Kahan:1996:BN

[137] W. Kahan. Beastly numbers. World-Wide Web document., January 13, 1996.URL http://www.cs.berkeley.edu/

~wkahan/tests/; http://www.cs.

berkeley.edu/~wkahan/tests/numbeast.

ps.

Kahan:1996:CAN

[138] W. Kahan. A computation with al-most no significance. Report, Depart-ment of Mathematics and Departmentof Electrical Engineering and ComputerScience, University of California, Berke-ley, Berkeley, CA, USA, May 6, 1996. 8pp. URL http://www.eecs.berkeley.

edu/~wkahan/CS279/Div754.pdf.

Kahan:1996:IPE

[139] W. Kahan. The improbability of prob-abilistic error analyses for numericalcomputations. Manuscript. This is anextended version of transparencies ti-tled “The Improbability of Probabilis-tic Error Analysis”, first presented inHamburg at the third ICIAM Congress,3–7 July, 1995., February 28, 1996.URL http://www.cs.berkeley.edu/~

wkahan/improber.ps.

Kahan:1996:LNS

[140] W. Kahan. Lecture notes on thestatus of IEEE Standard 754 for bi-nary floating-point arithmetic. World-Wide Web document., May 1996.URL http://www.cs.berkeley.edu/~

wkahan/ieee754status/ieee754.ps.

REFERENCES 21

Kahan:1996:TCR

[141] W. Kahan. A test for correctlyrounded SQRT. Lecture notes., 1996.URL http://www.cs.berkeley.edu/~

wkahan/SQRTest.ps.

Kahan:1996:WCY

[142] W. Kahan. What can you learn aboutfloating-point arithmetic in one hour?Postscript version accessible electron-ically at http://http.cs.berkeley.

edu/~wkahan/ieee754status., 1996.URL http://www.cs.berkeley.edu/~

wkahan/ieee754status/cs267fp.ps.

Zheng:1996:FSG

[143] Dao-Sheng Zheng. Further study andgeneralization of Kahan’s matrix exten-sion theorem. SIAM Journal on Ma-trix Analysis and Applications, 17(3):621–631, July 1996. CODEN SJMAEL.ISSN 0895-4798 (print), 1095-7162 (elec-tronic). See note [175].

Kahan:1997:CCR

[144] William Kahan and Ren-Cang Li. Com-position constants for raising the ordersof unconventional schemes for ordinarydifferential equations. Mathematics ofComputation, 66(219):1089–1099, July1997. CODEN MCMPAF. ISSN 0025-5718 (print), 1088-6842 (electronic).URL http://www.ams.org/jourcgi/

jour-pbprocess?fn=110&arg1=S0025-

5718-97-00873-9&u=/mcom/1997-66-

219/.

Kahan:1997:JNL

[145] W. Kahan. The John von Neumann lec-ture on the baleful effect of computerlanguages and benchmarks upon appliedmathematics, physics and chemistry.

World-Wide Web document., July 15,1997. URL http://www.cs.berkeley.

edu/~wkahan/SIAMjvnl.ps. Presentedat the SIAM 45th annual meeting, Stan-ford University.

Kahan:1997:LNS

[146] W. Kahan. Lecture notes on thestatus of IEEE Standard 754 for Bi-nary Floating-Point Arithmetic. World-Wide Web document, October 1, 1997.URL http://www.cs.berkeley.edu/~

wkahan/ieee754status/IEEE754.PDF.

Kahan:1997:MAA

[147] W. Kahan. Miscalculating area and an-gles of a needle-like triangle. Manu-script, July 1997.

Kahan:1997:RDI

[148] W. Kahan and Melody Y. Ivory. Round-off degrades an idealized cantilever.Technical report, Department of Mathe-matics and Department of Electrical En-gineering and Computer Science, Uni-versity of California, Berkeley, Berke-ley, CA, USA, July 3, 1997. 11 pp.URL http://www.cs.berkeley.edu/

~wkahan/Cantilever.pdf; http://

www.cs.berkeley.edu/~wkahan/Cantilever.

ps.

Kahan:1997:USC

[149] William Kahan and Ren-Chang Li. Un-conventional schemes for a class of ordi-nary differential equations—with appli-cations to the Korteweg–de Vries equa-tion. Journal of computational physics,134(2):316–331, July 1, 1997. CO-DEN JCTPAH. ISSN 0021-9991 (print),1090-2716 (electronic). URL http:

//www.sciencedirect.com/science/

article/pii/S0021999197957107.

REFERENCES 22

Woehr:1997:CWK

[150] Jack Woehr. A conversation withWilliam Kahan: How important is nu-merical accuracy? Dr. Dobb’s Jour-nal of Software Tools, 22(11):18–20, 22,24, 26, 30, 32, November 1997. CO-DEN DDJOEB. ISSN 1044-789X. Ka-han, the father of the IEEE 754 floating-point standard, talks about floating-point arithmetic issues, and numericaldeficiencies in Java.

Xie:1997:NDK

[151] Jianjun Xie. A note on the Davis-Kahan sin Θ theorem. Linear Algebraand its Applications, 258(1–3):129–135,June ??, 1997. CODEN LAAPAW.ISSN 0024-3795 (print), 1873-1856 (elec-tronic). URL http://www.elsevier.

com/cgi-bin/cas/tree/store/laa/


1997&volume=258&issue=1-3&aid=9600207.

Darcy:1998:APE

[152] Joseph D. Darcy and William Kahan.Analysis of Proposal for Extension toJava Floating Point Semantics, Revision1. Technical report, Java Grande Nu-merics Working Group, August 7, 1998.18 pp. URL http://www.sonic.net/~

jddarcy/Research/jgrande.pdf.

Kahan:1998:AFE

[153] W. Kahan. Answers for final examina-tion. World-Wide Web document, De-cember 19, 1998. URL http://www.


finexms.pdf. Lecture notes for MathH110.

Kahan:1998:CTL

[154] W. Kahan. Chio’s trick for linear equa-tions with integer coefficients. World-

Wide Web document, October 24, 1998.URL http://www.cs.berkeley.edu/~

wkahan/MathH110/chio.pdf. Lecturenotes for Math H110.

Kahan:1998:DP

[155] W. Kahan. Diagonal prominence.World-Wide Web document, Octo-ber 25, 1998. URL http://www.


diagprom.pdf. Lecture notes for MathH110.

Kahan:1998:GEO

[156] W. Kahan. Geometry of elementary op-erations. World-Wide Web document,September 22, 1998. URL http://www.


geo.pdf. Lecture notes for Math H110.

Kahan:1998:GJI

[157] W. Kahan. Gauss–Jordan inversion ofa matrix. World-Wide Web document,October 16, 1998. URL http://www.


gji.pdf. Lecture notes for Math H110.

Kahan:1998:HJFa

[158] W. Kahan and Joseph D. Darcy.How Java’s floating-point hurts ev-eryone everywhere. Technical re-port, Department of Mathematics andDepartment of Electrical Engineer-ing and Computer Science, Univer-sity of California, Berkeley, Berkeley,CA, USA, June 18, 1998. 80 pp.URL http://www.cs.berkeley.edu/

~wkahan/JAVAhurt.pdf; http://

www.cs.berkeley.edu/~wkahan/JAVAhurt.

ps.

Kahan:1998:HJFb

[159] William Kahan. How Java’s floating-point hurts everyone everywhere. In

REFERENCES 23

ACM [324], page ?? CODEN CPEXEI.ISSN 1040-3108 (print), 1096-9128 (elec-tronic). LCCN ???? URL http://www.

cs.ucsb.edu/conferences/java98/

papers/javahurt.pdf. Also publishedas Concurrency: Practice and Experi-ence, 10(11–13), September 1998, CO-DEN CPEXEI, ISSN 1040-3108.

Kahan:1998:IPE

[160] W. Kahan. The improbability of proba-bilistic error analyses for numerical com-putations. Technical report, Depart-ment of Mathematics and Departmentof Electrical Engineering and ComputerScience, University of California, Berke-ley, Berkeley, CA, USA, June 10, 1998.34 pp. URL http://www.cs.berkeley.

edu/~wkahan/improber.pdf.

Kahan:1998:JFD

[161] W. Kahan. Jacobi’s formula for thederivative of a determinant. World-Wide Web document, October 14, 1998.URL http://www.cs.berkeley.edu/~

wkahan/MathH110/jacobi.pdf. Lec-ture notes for Math H110.

Kahan:1998:LNR

[162] W. Kahan. Lecture notes on real root-finding. World-Wide Web document,March 4, 1998. URL http://www.


LNRRabst.txt. Lecture notes for Math128.

Kahan:1998:LRR

[163] W. Kahan. A lecture on real root-finding. World-Wide Web document,April 6, 1998. URL http://www.


LecRlRtF.pdf. Lecture notes for Math128. Extracted from “Lecture Notes onReal Root-Finding” [162].

Kahan:1998:LSA

[164] W. Kahan. Least-squares approxima-tion and bilinear forms. World-WideWeb document, September 20, 1998.URL http://www.cs.berkeley.edu/~

wkahan/MathH110/lstsqrs.pdf. Lec-ture notes for Math H110.

Kahan:1998:MLN

[165] W. Kahan. Matlab’s loss is no-body’s gain. Technical report, De-partment of Mathematics and De-partment of Electrical Engineeringand Computer Science, University ofCalifornia, Berkeley, Berkeley, CA,USA, August 23, 1998. 35 pp.URL http://www.cs.berkeley.edu/

~wkahan/MxMulEps.pdf; http://

www.cs.berkeley.edu/~wkahan/MxMulEps.

ps.

Kahan:1998:NDS

[166] W. Kahan. Notes on 2-dimensionalspaces. World-Wide Web document,October 4, 1998. URL http://www.


2dspaces.pdf. Lecture notes for MathH110.

Kahan:1998:PSP

[167] W. Kahan. Problem set 1: Prob-lems about our axioms for a vectorspace. World-Wide Web document,September 16, 1998. URL http://www.


prblms1.pdf. Lecture notes for MathH110.

Kahan:1998:RRE

[168] W. Kahan. The reduced row-echelon form is unique. World-WideWeb document, September 12, 1998.

REFERENCES 24


wkahan/MathH110/RREF1.pdf. Lecturenotes for Math H110.

Kahan:1998:SPS

[169] W. Kahan. Solutions for problem set 2.World-Wide Web document, October 1,1998. URL http://www.cs.berkeley.

edu/~wkahan/MathH110/prblms2.pdf.Lecture notes for Math H110.

Kahan:1998:THT

[170] W. Kahan. Take-home test’s solu-tions. World-Wide Web document,October 5, 1998. URL http://www.


tkhms.pdf. Lecture notes for MathH110.

Kahan:1998:TPS

[171] W. Kahan. Test problems and solu-tions. World-Wide Web document, De-cember 4, 1998. URL http://www.


testexam.pdf. Lecture notes for MathH110.

Kahan:1998:VSB

[172] W. Kahan. Vector spaces, bases, anddual spaces. World-Wide Web docu-ment, November 4, 1998. URL http://

www.cs.berkeley.edu/~wkahan/MathH110/

pts.pdf. Lecture notes for Math H110.

Severance:1998:IOM

[173] Charles Severance. An interview withthe old man of floating-point. Remi-niscences elicited from William Kahan.World-Wide Web document., February1998. URL http://www.cs.berkeley.

edu/~wkahan/ieee754status/754story.

html. A shortened version appears in[174].

Severance:1998:SII

[174] Charles Severance. Standards: IEEE754: An interview with William Kahan.Computer, 31(3):114–115, March 1998.CODEN CPTRB4. ISSN 0018-9162(print), 1558-0814 (electronic). URLhttp://pdf.computer.org/co/books/

co1998/pdf/r3114.pdf.

Zheng:1998:NFS

[175] Dao-Sheng Zheng. Note on “Fur-ther Study and Generalization of Ka-han’s Matrix Extension Theorem”.SIAM Journal on Matrix Analysis andApplications, 19(1):277–278, January1998. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic).URL http://epubs.siam.org/sam-

bin/dbq/article/31443. See [143].

Anonymous:1999:AAM

[176] Anonymous. ACM Alan M. TuringAward: William V. Kahan. World WideWeb document, February 8, 1999. URLhttp://www.acm.org/awards/turing_

citations/kahan.html.

Kahan:1999:C

[177] W. Kahan. Computing xn. World-Wide Web document, March 20, 1999.URL http://www.cs.berkeley.edu/~

wkahan/Math55/npower.pdf. Lecturenotes for Math 55.

Kahan:1999:CS

[178] W. Kahan. Coins and stamps. World-Wide Web document, May 1, 1999.URL http://www.cs.berkeley.edu/~

wkahan/Math55/coins.pdf. Lecturenotes for Math 55.

REFERENCES 25

Kahan:1999:CSC

[179] W. Kahan. Conic sections inthe complex z-plane. World-WideWeb document, September 4, 1999.URL http://www.cs.berkeley.edu/~

wkahan/Math185/conics.pdf. Lecturenotes for Math 185.

Kahan:1999:CSL

[180] W. Kahan. California super lottery.World-Wide Web document, April 13,1999. URL http://www.cs.berkeley.

edu/~wkahan/Math55/lotto.pdf. Lec-ture notes for Math 55.

Kahan:1999:CVC

[181] W. Kahan. Complexity vs. cost. World-Wide Web document, August 24, 1999.URL http://www.cs.berkeley.edu/~

wkahan/Math55/cmplxty.pdf. Lecturenotes for Math 55.

Kahan:1999:D

[182] W. Kahan. Derangements. World-Wide Web document, June 9, 1999.URL http://www.cs.berkeley.edu/~

wkahan/Math55/derange.pdf. Lecturenotes for Math 55.

Kahan:1999:DTP

[183] W. Kahan. Discussion of two prob-lems in the text. World-WideWeb document, February 3, 1999.URL http://www.cs.berkeley.edu/~

wkahan/Math55/m55jan28.pdf. Lec-ture notes for Math 55.

Kahan:1999:EGA

[184] W. Kahan. Euclid’s GCD algorithm.World-Wide Web document, May 10,1999. URL http://www.cs.berkeley.

edu/~wkahan/Math55/gcd.pdf. Lec-ture notes for Math 55.

Kahan:1999:EMSa

[185] W. Kahan. Exam model solutions.World-Wide Web document, Febru-ary 10, 1999. URL http://www.


feb10s.pdf. Lecture notes for Math 55.

Kahan:1999:EMSb

[186] W. Kahan. Exam: Model solutions.World-Wide Web document, March 3,1999. URL http://www.cs.berkeley.

edu/~wkahan/Math55/m55mar3s.pdf.Lecture notes for Math 55.

Kahan:1999:EMSc

[187] W. Kahan. Exam: Model solutions.World-Wide Web document, March 18,1999. URL http://www.cs.berkeley.

edu/~wkahan/Math55/m55mr18s.pdf.Lecture notes for Math 55.

Kahan:1999:EMSd

[188] W. Kahan. Exam: Model solutions.World-Wide Web document, May 11,1999. URL http://www.cs.berkeley.

edu/~wkahan/Math55/m55my11s.pdf.Lecture notes for Math 55.

Kahan:1999:EPI

[189] W. Kahan. Enumerating pairs of in-tegers. World-Wide Web document,April 30, 1999. URL http://www.


pairs.pdf. Lecture notes for Math 55.

Kahan:1999:FEM

[190] W. Kahan. Final exam: Model so-lutions. World-Wide Web document,May 14, 1999. URL http://www.


m55finls.pdf. Lecture notes for Math55.

REFERENCES 26

Kahan:1999:FI

[191] W. Kahan. The fragility of improb-ability. World-Wide Web document,June 9, 1999. URL http://www.


correln.pdf. Lecture notes for Math55.

Kahan:1999:FLT

[192] W. Kahan. Fermat’s little theo-rem. World-Wide Web document,March 1, 1999. URL http://www.


fermat.pdf. Lecture notes for Math 55.

Kahan:1999:HP

[193] W. Kahan. The halting problem. World-Wide Web document, March 13, 1999.URL http://www.cs.berkeley.edu/~

wkahan/Math55/halting.pdf. Lecturenotes for Math 55.

Kahan:1999:LLN

[194] W. Kahan. The Law of Large Numbers.World-Wide Web document, May 29,1999. URL http://www.cs.berkeley.

edu/~wkahan/Math55/largenos.pdf.Lecture notes for Math 55.

Kahan:1999:MS

[195] W. Kahan. Math 55 syllabus. World-Wide Web document, June 20, 1999.URL http://www.cs.berkeley.edu/~

wkahan/Math55/syllabus.pdf. Lec-ture notes for Math 55.

Kahan:1999:MSS

[196] W. Kahan. Math 55 Spring 1999 syl-labus. World-Wide Web document,May 6, 1999. URL http://www.


math55.pdf. Lecture notes for Math 55.

Kahan:1999:OCT

[197] W. Kahan. Only commutators havetrace zero. World-Wide Web docu-ment, June 10, 1999. URL http://www.


trace0.pdf. Lecture notes for MathH110.

Kahan:1999:PS

[198] W. Kahan. Problems’ solutions. World-Wide Web document, December 15,1999. URL http://www.cs.berkeley.

edu/~wkahan/Math185/probsoln.pdf.Lecture notes for Math 185.

Kahan:1999:RAI

[199] W. Kahan. Rational approximationsof irrationals. World-Wide Web docu-ment, April 8, 1999. URL http://www.


p249n17.pdf. Lecture notes for Math55.

Kahan:1999:SCD

[200] W. Kahan and Richard J. Fateman.Symbolic computation of divided differ-ences. SIGSAM Bulletin (ACM Spe-cial Interest Group on Symbolic and Al-gebraic Manipulation), 33(2):7–28, June1999. CODEN SIGSBZ. ISSN 0163-5824(print), 1557-9492 (electronic).

Kahan:1999:SFE

[201] W. Kahan. Solutions for final exam.World-Wide Web document, Decem-ber 11, 1999. URL http://www.


xm11decs.pdf. Lecture notes for Math185.

Kahan:1999:SI

[202] W. Kahan. Some inequalities. World-Wide Web document, May 9, 1999.

REFERENCES 27


wkahan/Math55/ineq.pdf. Lecturenotes for Math 55.

Kahan:1999:SP

[203] W. Kahan. Solutions to problems.World-Wide Web document, Decem-ber 12, 1999. URL http://www.


31aug99s.pdf. Lecture notes for Math185.

Kahan:1999:SPH

[204] W. Kahan. Solutions to problemsin H. W. Lenstra’s notes. World-Wide Web document, July 9, 1999.URL http://www.cs.berkeley.edu/~

wkahan/Math55/lenstras.pdf. Lec-ture notes for Math 55.

Kahan:1999:SRD

[205] W. Kahan. Square root without division.World-Wide Web document, Febru-ary 23, 1999. URL http://www.cs.

berkeley.edu/~wkahan/ieee754status/

reciprt.pdf.

Kahan:1999:SSE

[206] W. Kahan. SOLVEzag: Solve the equa-tion z = (1 − exp(−pz))/(pz) for z ≥0 as a function of p ≥ 0. World-Wide Web document, August 1, 1999.URL http://www.cs.berkeley.edu/

~wkahan/Math128/SOLVEzag.pdf;

http://www.cs.berkeley.edu/~wkahan/

Math128/SOLVEzag.ps. Lecture notesfor Math 128.

Kahan:1999:T

[207] W. Kahan. Test. World-WideWeb document, January 27, 1999.URL http://www.cs.berkeley.edu/~

wkahan/Math55/jan27s.pdf. Lecturenotes for Math 55.

Kahan:1999:TMS

[208] W. Kahan. Test: Model solutions.World-Wide Web document, April 26,1999. URL http://www.cs.berkeley.

edu/~wkahan/Math55/m55ap26s.pdf.Lecture notes for Math 55.

Kahan:1999:TPA

[209] W. Kahan. Three problems aboutcombinatorial coefficients. World-Wide Web document, April 26, 1999.URL http://www.cs.berkeley.edu/~

wkahan/Math55/ncr.pdf. Lecture notesfor Math 55.

Kahan:1999:WB

[210] W. Kahan. Waiting for a bus. World-Wide Web document, April 12, 1999.URL http://www.cs.berkeley.edu/~

wkahan/Math55/bus.pdf. Lecture notesfor Math 55.

Bhatia:2000:PNS

[211] Rajendra Bhatia, William Kahan, andRen-Cang Li. Pinchings and norms ofscaled triangular matrices. TechnicalReport 2000-23, Department of Mathe-matics, University of Kentucky, Lexing-ton, KY, USA, 2000. URL http://www.

cs.uky.edu/~rcli/papers/kablrep.

ps.

Bindel:2000:CGR

[212] D. Bindel, J. Demmel, W. Kahan,and O. Marques. On computingGivens rotations reliably and effi-ciently. LAPACK Working Note148, Department of Computer Sci-ence, University of Tennessee, Knoxville,Knoxville, TN 37996, USA, October2000. URL http://www.netlib.org/

lapack/lawns/lawn148.ps; http:

//www.netlib.org/lapack/lawnspdf/

REFERENCES 28

lawn148.pdf. UT-CS-00-449, October2000. Published in [242].

He:2000:PAA

[213] Yun (Helen) He and Chris H. Q.Ding. Platforms: An accurate arith-metics approach. In ACM [325], page150. ISBN 0-7803-9802-5. LCCNQA76.88 2000. URL http://csdl.

computer.org/comp/proceedings/sc/

2000/9802/00/9802toc.htm; http:

//www.sc2000.org/proceedings/info/

fp.pdf.

Kahan:2000:AFE

[214] W. Kahan. Answers for final examina-tion. World-Wide Web document, De-cember 21, 2000. URL http://www.


finals.pdf. Lecture notes for MathH110.

Kahan:2000:AFV

[215] W. Kahan. Axioms for fields and vec-tor spaces. World-Wide Web docu-ment, May 17, 2000. URL http://www.


Axioms.pdf. Lecture notes for MathH110.

Kahan:2000:CPR

[216] W. Kahan. Cross-products and rota-tions in 2- and 3-dimensional Euclideanspaces: Notes for math. H110. World-Wide Web document, October 11, 2000.URL http://www.cs.berkeley.edu/~

wkahan/Math128/Cross.pdf. Lecturenotes for Math 128.

Kahan:2000:EGA

[217] W. Kahan. Euclid’s GCD algo-rithm. World-Wide Web document,

October 5, 2000. URL http://www.


gcd5.pdf. Lecture notes for Math H110.

Kahan:2000:GEO

[218] W. Kahan. Geometry of elementaryoperations and subspaces: A contin-uation of notes titled “geometry ofelementary operations”. World-WideWeb document, December 14, 2000.URL http://www.cs.berkeley.edu/~

wkahan/MathH110/geos.pdf. Lecturenotes for Math H110.

Kahan:2000:GMH

[219] W. Kahan. Grades for Math. H110.World-Wide Web document, 2000.URL http://www.cs.berkeley.edu/~

wkahan/MathH110/h110_00.pdf. Lec-ture notes for Math H110.

Kahan:2000:HRQ

[220] W. Kahan. How to recognize a quadraticform. World-Wide Web document, Oc-tober 31, 2000. URL http://www.cs.

berkeley.edu/~wkahan/MathH110/qf.

pdf. Lecture notes for Math H110.

Kahan:2000:JNF

[221] W. Kahan. Jordan’s normal form.World-Wide Web document, Decem-ber 7, 2000. URL http://www.


jordan.pdf. Lecture notes for MathH110.

Kahan:2000:LAM

[222] W. Kahan. Linear algebra and ma-trix theory. World-Wide Web docu-ment, Fall 2000. URL http://www.


Topics.pdf. Lecture notes for MathH110.

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Kahan:2000:MAA

[223] W. Kahan. Miscalculating area and an-gles of a needle-like triangle. World-Wide Web lecture notes for introductorynumerical analysis classes., March 24,2000. URL http://www.cs.berkeley.

edu/~wkahan/Triangle.pdf.

Kahan:2000:MVM

[224] W. Kahan. Marketing versus math-ematics and other ruminations onthe design of floating-point arith-metic. Technical report, Mathemat-ics Department and Electrical Engi-neering and Computer Science Depart-ment, University of California, Berke-ley, Berkeley, CA, USA, August 27,2000. 48 pp. URL http://www.

cs.berkeley.edu/~wkahan/MktgMath.

pdf; http://www.cs.nyu.edu/cs/

faculty/overton/book/docs/KahanTalk.

pdf.

Kahan:2000:NJI

[225] W. Kahan. Notes on Jensen’s in-equality for Math. H90. World-WideWeb document, September 27, 2000.URL http://www.cs.berkeley.edu/~

wkahan/MathH110/jensen.pdf. Lec-ture notes for Math H110.

Kahan:2000:NVN

[226] W. Kahan. Notes on vector norms.World-Wide Web document, Decem-ber 6, 2000. URL http://www.


normlite.pdf. Lecture notes for MathH110.

Kahan:2000:PSa

[227] W. Kahan. Problems’ solutions. World-Wide Web document, October 19, 2000.


wkahan/MathH110/s10oct.pdf. Lec-ture notes for Math H110.

Kahan:2000:PSb

[228] W. Kahan. Problems’ solutions. World-Wide Web document, November 27,2000. URL http://www.cs.berkeley.

edu/~wkahan/MathH110/s21nov.pdf.Lecture notes for Math H110.

Kahan:2000:RDFa

[229] W. Kahan. Ruminations on thedesign of floating-point arithmetic.World-Wide Web document, April25, 2000. URL http://cs.nyu.

edu/cs/faculty/overton/book/docs/

KahanTalk.pdf.

Kahan:2000:RDFb

[230] W. Kahan. Marketing versus math-ematics and other ruminations onthe design of floating-point arith-metic. Technical report, Mathemat-ics Department and Electrical Engi-neering and Computer Science Depart-ment, University of California, Berke-ley, Berkeley, CA, USA, August 27,2000. 48 pp. URL http://www.cs.

berkeley.edu/%7Ewkahan/MktgMath.

pdf; http://www.cs.nyu.edu/cs/

faculty/overton/book/docs/KahanTalk.

pdf.

Kahan:2000:TCE

[231] W. Kahan. Topics covered for exampurposes. World-Wide Web document,December 12, 2000. URL http://www.


covered.pdf. Lecture notes for MathH110.

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Li:2000:DIT

[232] X. S. Li, J. W. Demmel, D. H. Bai-ley, G. Henry, Y. Hida, J. Iskandar,W. Kahan, A. Kapur, M. C. Martin,T. Tung, and D. J. Yoo. Design, im-plementation and testing of extendedand mixed precision BLAS. LAPACKWorking Note and University of Ten-nessee report 149 and CS-00-451, De-partment of Computer Science, Univer-sity of Tennessee, Knoxville, Knoxville,TN 37996, USA, October 2000. 61pp. URL http://www.netlib.org/



lawn149.pdf.

Demmel:2001:CAF

[233] J. Demmel, Ben Diament, W. Kahan,Plamen Koev, Ming Gu, Stan Eisen-stat, Ivan Slapnicar, Kresimir Veselic,and Zlatko Drmac. The complexityof accurate floating point computationand symbolic computing, or, can wedo numerical linear algebra in poly-nomial time? Lecture slides, 2001.URL http://www.cs.berkeley.edu/~

demmel/ISSAC2001_2.pdf.

Kahan:2001:ATA

[234] W. Kahan. Approximate trisec-tion of an angle. World-WideWeb document, January 31, 2001.URL http://www.cs.berkeley.edu/~

wkahan/trisect.pdf; http://www.

cs.berkeley.edu/~wkahan/trisect.

ps.

Kahan:2001:HBM

[235] W. Kahan. How blabber-mouth U-boatsgot sunk in World War II. World-WideWeb document, November 24, 2001.


wkahan/BlaUboat.pdf.

Kahan:2001:MBR

[236] W. Kahan. M. Brand’s 2nd re-vised problem has infinitely many so-lutions. World-Wide Web document,April 13, 2001. URL http://www.


Brand2.pdf. Lecture notes for Math128.

Kahan:2001:NSF

[237] W. Kahan. Names for standard-ized floating-point formats. Techni-cal report, Mathematics Departmentand Electrical Engineering and Com-puter Science Department, Univer-sity of California, Berkeley, Berke-ley, CA, USA, May 17, 2001. 4 pp.URL http://www.cs.berkeley.edu/~

wkahan/ieee754status/Names.pdf.

Kahan:2001:SFP

[238] W. Kahan. SRTEST: A Fortran pro-gram to test any SRT divider’s logicfor quotient-digit selection. World-Wide Web document, August 6, 2001.URL http://www.cs.berkeley.edu/~

wkahan/srtest/.

Kahan:2001:WDW

[239] W. Kahan. Why do we need a floating-point arithmetic standard? Technicalreport, University of California, Berke-ley, CA, USA, March 2001. 49 pp.URL http://www.cs.berkeley.edu/

~wkahan/ieee754status/why-ieee.

pdf.

Kahan:2001:WVT

[240] W. Kahan. What has the volumeof a tetrahedron to do with computer

REFERENCES 31

programming languages? Techni-cal report, Department of Mathemat-ics and Department of Electrical En-gineering and Computer Science, Uni-versity of California, Berkeley, Berke-ley, CA, USA, April 20, 2001. 31 pp.URL http://www.cs.berkeley.edu/~

wkahan/VtetLang.pdf.

Bhatia:2002:PNS

[241] Rajendra Bhatia, William Kahan, andRen-Cang Li. Pinchings and norms ofscaled triangular matrices. Linear Mul-tilinear Algebra, 50(1):15–21, 2002. CO-DEN LNMLAZ. ISSN 0308-1087.

Bindel:2002:CGR

[242] David Bindel, James Demmel, WilliamKahan, and Osni Marques. On com-puting Givens rotations reliably and ef-ficiently. ACM Transactions on Math-ematical Software, 28(2):206–238, June2002. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic).

Kahan:2002:AI

[243] W. Kahan. About infinity. World-Wide Web document, March 7, 2002.URL http://www.cs.berkeley.edu/~

wkahan/Infinity.pdf.

Kahan:2002:ALN

[244] W. Kahan. Abbreviated lecture noteson ellipsoidal error bounds for trajectorycalculations. World-Wide Web docu-ment, March 9, 2002. URL http://www.


Ellipsoi.pdf. Lecture notes for Math128.

Kahan:2002:CA

[245] W. Kahan. Computing an adju-gate. World-Wide Web document,

March 19, 2002. URL http://www.


Adjx.pdf. Lecture notes for Math H110.

Kahan:2002:FPC

[246] W. Kahan. Fclass: a proposed clas-sification of standard floating-pointoperands. World-Wide Web docu-ment, March 23, 2002. URL http:

//www.cs.berkeley.edu/%7Ewkahan/

ieee754status/Fclass.pdf.

Kahan:2002:HGI

[247] W. Kahan. Huge generalized inversesof rank-deficient matrices. World-Wide Web document, May 2, 2002.URL http://www.cs.berkeley.edu/~

wkahan/MathH110/GIlite.pdf. Lec-ture notes for Math H110.

Kahan:2002:IBD

[248] W. Kahan. Idempotent binary → dec-imal → binary conversion. World-Wide Web document, February 2, 2002.URL http://www.cs.berkeley.edu/~

wkahan/Math128/BinDecBin.pdf. Lec-ture notes for Math 128.

Kahan:2002:MFE

[249] W. Kahan. Math. 110 final exam.World-Wide Web document, May 27,2002. URL http://www.cs.berkeley.

edu/~wkahan/MathH110/Final02.pdf.Lecture notes for Math H110.

Kahan:2002:MIH

[250] W. Kahan. Matlab’s inverses of Hilbertmatrices. World-Wide Web document,May 2, 2002. URL http://www.


HilbMats.pdf. Lecture notes for MathH110.

REFERENCES 32

Kahan:2002:MPI

[251] W. Kahan. Matlab programs for in-terpolation and extrapolation. World-Wide Web document, February 11,2002. URL http://www.cs.berkeley.

edu/~wkahan/Math128/XPOLATE. Lec-ture notes for Math 128.

Kahan:2002:MTa

[252] W. Kahan. Midterm test. World-Wide Web document, March 5, 2002.URL http://www.cs.berkeley.edu/~

wkahan/MathH110/MidTerm.pdf. Lec-ture notes for Math H110.

Kahan:2002:MTb

[253] W. Kahan. Midterm test. World-Wide Web document, April 29, 2002.URL http://www.cs.berkeley.edu/~

wkahan/MathH110/MidTerm2.pdf. Lec-ture notes for Math H110.

Kahan:2002:NAC

[254] W. Kahan. The numerical analyst ascomputer science curmudgeon. World-Wide Web document, September 11,2002. URL http://www.cs.berkeley.

edu/~wkahan/Curmudge.pdf.

Kahan:2002:ODE

[255] W. Kahan. An ordinary differentialequation in interval-arithmetic. World-Wide Web document, March 9, 2002.URL http://www.cs.berkeley.edu/~

wkahan/Math128/ODEintvl.pdf. Lec-ture notes for Math 128.

Kahan:2002:RPR

[256] W. Kahan. Refineig: a pro-gram to refine eigensystems. World-Wide Web document, May 29, 2002.URL http://www.cs.berkeley.edu/

~wkahan/Math128/refineig.abs;


Math128/RefinEig.pdf. Lecture notesfor Math 128. Work in progress: not forredistribution.

Kahan:2002:SCP

[257] W. Kahan. Separation of clouds bya plane. World-Wide Web document,May 17, 2002. URL http://www.


Separate.pdf; http://www.cs.berkeley.

edu/~wkahan/MathH110/Separate.pdf.Lecture notes for Math H110 and Math128.

Kahan:2002:TPM

[258] W. Kahan. Two problems: Must tri-angular matrices have triangular in-verses? When are triangular fac-torizations unique? World-WideWeb document, February 20, 2002.URL http://www.cs.berkeley.edu/~

wkahan/MathH110/TriFact.pdf. Lec-ture notes for Math H110.

Kahan:2002:TRD

[259] W. Kahan. Thiele’s reciprocal dif-ferences and derivatives. World-WideWeb document, February 14, 2002.URL http://www.cs.berkeley.edu/~

wkahan/Math128/THIELEDF. Lecturenotes for Math 128.

Li:2002:DIT

[260] Xiaoye S. Li, James W. Demmel,David H. Bailey, Greg Henry, YozoHida, Jimmy Iskandar, William Kahan,Suh Y. Kang, Anil Kapur, Michael C.Martin, Brandon J. Thompson, TeresaTung, and Daniel J. Yoo. Design, imple-mentation and testing of extended andmixed precision BLAS. ACM Transac-tions on Mathematical Software, 28(2):152–205, June 2002. CODEN ACMSCU.

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Parlett:2002:QA

[261] Beresford N. Parlett. The QR algo-rithm. World-Wide Web document,April 22, 2002. URL http://www.


Parlett.pdf. Lecture notes for Math128.

Shampine:2002:MOS

[262] Lawrence F. Shampine and Mark W. Re-ichelt. The Matlab ODE suite. World-Wide Web document, February 27,2002. URL http://www.cs.berkeley.

edu/~wkahan/Math128/ODEsuite.pdf.Lecture notes for Math 128.

Kahan:2003:CPR

[263] W. Kahan. Cross-products and rota-tions in 2- and 3-dimensional Euclideanspaces. World-Wide Web document,November 23, 2003. URL http://www.


Cross.pdf. Lecture notes for MathH110.

Randolph:2003:WKT

[264] Dan W. Randolph. William Kahan:1989 Turing Award winner. Cosc5000 class report, Department of Com-puter Science University of Wyoming,Laramie, WY, USA, May 16, 2003. 7pp. URL http://www.mapsharecorp.

com/kahan.pdf.

Kahan:2004:A

[265] W. Kahan. Abstracts. World-WideWeb document, November 1, 2004.URL http://www.cs.berkeley.edu/~

wkahan/abstrcts. Abstracts of some ofthe online documents.

Kahan:2004:ASC

[266] W. Kahan. Assignment: Solve A4z =b by conjugate gradient iteration with-out ever storing the matrix A4. World-Wide Web document, April 19, 2004.URL http://www.cs.berkeley.edu/~

wkahan/Math128/a4d2.txt. Lecturenotes for Math 128.

Kahan:2004:ASE

[267] W. Kahan. Angle subtended at theeye by neighboring stars. World-WideWeb document, September 17, 2004.URL http://www.cs.berkeley.edu/~

wkahan/Math128/angle.pdf. Lecturenotes for Math 128.

Kahan:2004:CFP

[268] W. Kahan. On the cost of floating-point computation without extra-precisearithmetic. World-Wide Web document,November 20, 2004. URL http://www.

cs.berkeley.edu/~wkahan/Qdrtcs.

pdf. See [304] for a proof of this al-gorithm for accurate computation of thediscriminant needed for the solution ofquadratic equations.

Kahan:2004:DCP

[269] W. Kahan. Derivatives in the com-plex z-plane. World-Wide Web docu-ment, May 26, 2004. URL http://www.


Derivative.pdf. Lecture notes forMath 185.

Kahan:2004:FMD

[270] W. Kahan. Failure mode: Do MAT-LAB’s lu(. . . ), inv(. . .), / and \

have a failure mode? World-WideWeb document, February 17, 2004.URL http://www.cs.berkeley.edu/~

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wkahan/Math128/FailMode.pdf. Lec-ture notes for Math 128.

Kahan:2004:HFM

[271] W. Kahan. How futile are mind-less assessments of roundoff in floating-point computation? World-WideWeb document, November 1, 2004.URL http://www.cs.berkeley.edu/

~wkahan/Mind1ess.pdf; http://

www.cs.berkeley.edu/~wkahan/Mindless.

pdf.

Kahan:2004:ICG

[272] W. Kahan. Iterate: Conjugate gra-dients and overrelaxation. World-Wide Web document, April 7, 2004.URL http://www.cs.berkeley.edu/~

wkahan/Math128/Iterate.pdf. Lec-ture notes for Math 128.

Kahan:2004:LNR

[273] W. Kahan. Lecture notes on real root-finding. World-Wide Web document,June 23, 2004. URL http://www.


RealRoots.pdf. Lecture notes for Math128. Work in progress: not for redistri-bution.

Kahan:2004:LTC

[274] W. Kahan. A logarithm too cleverby half. World-Wide Web document,August 9, 2004. URL http://www.

cs.berkeley.edu/~wkahan/LOG10HAF.

TXT.

Kahan:2004:PMG

[275] W. Kahan. Prof. Ming Gu’s trans-parencies. World-Wide Web document,May 5, 2004. URL http://www.cs.

berkeley.edu/~wkahan/Math128/MGu;


Math128/MGu/kahanbvp.pdf; http:

//www.cs.berkeley.edu/~wkahan/Math128/

MGu/kahanss.pdf; http://www.cs.

berkeley.edu/~wkahan/Math128/MGu/

pendi.pdf; http://www.cs.berkeley.

edu/~wkahan/Math128/MGu/tridi.pdf.Lecture notes for Math 128.

Kahan:2004:SSR

[276] W. Kahan. 128 squares of 128 squareroots. World-Wide Web document,January 29, 2004. URL http://www.


SqSqrts.pdf. Lecture notes for Math128.

Kahan:2004:THT

[277] W. Kahan. Take-home test for math.128B. World-Wide Web document,March 8, 2004. URL http://www.


M128Bprob5Mar04.pdf. Lecture notesfor Math 128.

Kahan:2004:TPM

[278] W. Kahan. Three problems for math.128B. World-Wide Web document,February 10, 2004. URL http://www.


M128Bsoln09Feb04.pdf. Lecture notesfor Math 128.

Kahan:2004:TSC

[279] W. Kahan. Is there a skew Cayleytransform with zero diagonal? World-Wide Web document, August 6, 2004.URL http://www.cs.berkeley.edu/~

wkahan/skcayley.pdf.

Kahan:2004:TSD

[280] W. Kahan. Taylor series for differen-tial equation solvers’ local error. World-Wide Web document, August 25, 2004.URL http://www.cs.berkeley.edu/~

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wkahan/Math128/Truncate.pdf. Lec-ture notes for Math 128.

Anonymous:2005:MGP

[281] Anonymous. The Mathematics Geneal-ogy Project: William Morton Kahan.World-Wide Web document, 2005. URLhttp://genealogy.math.ndsu.nodak.

edu/html/id.phtml?id=16049.

Demmel:2005:EBE

[282] James Demmel, Yozo Hida, W. Ka-han, Xiaoye S. Li, Soni Mukher-jee, and E. Jason Riedy. Errorbounds from extra precise iterative re-finement. LAPACK Working Note165, Department of Computer Sci-ence, University of Tennessee, Knoxville,Knoxville, TN 37996, USA, February2005. URL http://www.netlib.org/



lawn165.pdf. UT-CS-05-547, February2005.

Kahan:2005:BTG

[283] William Kahan. A brief tutorialon gradual underflow. World-WideWeb lecture notes., July 8, 2005.URL http://www.cs.berkeley.edu/~

wkahan/ARITH_17U.pdf. Prepared forARITH 17, Tues. 28 June 2005, and sub-sequently augmented.

Kahan:2005:DP

[284] William Kahan. A Demonstration ofPresubstitution for ∞/∞, July 5, 2005.10 pp. URL http://www.cs.berkeley.

edu/~wkahan/Grail.pdf.

Kahan:2005:FPA

[285] William Kahan. Floating-point arith-metic besieged by “business deci-sions”. World-Wide Web lecture notes.,

July 5, 2005. URL http://www.

cs.berkeley.edu/~wkahan/ARITH_17.

pdf. A Keynote Address, prepared forthe IEEE-Sponsored ARITH 17 Sympo-sium on Computer Arithmetic, deliveredon Mon. 27 June 2005 in Hyannis, Mas-sachusetts.

Kahan:2005:OQD

[286] William Kahan and Dan Zuras. Anopen question to developers of nu-merical software. Computer, 38(5):91–94, May 2005. CODEN CP-TRB4. ISSN 0018-9162 (print),1558-0814 (electronic). URL http:

//csdl.computer.org/comp/mags/co/

2005/05/r5091abs.htm; http://

csdl.computer.org/comp/mags/co/

2005/05/r5toc.htm; http://csdl.

computer.org/dl/mags/co/2005/05/

r5091.pdf.

Demmel:2006:EBE

[287] James Demmel, Yozo Hida, William Ka-han, Xiaoye S. Li, Sonil Mukherjee, andE. Jason Riedy. Error bounds fromextra-precise iterative refinement. ACMTransactions on Mathematical Software,32(2):325–351, June 2006. CODENACMSCU. ISSN 0098-3500 (print),1557-7295 (electronic).

Kahan:2006:AIR

[288] William Kahan. Applications of IEEE754r’s rounding modes. World-WideWeb document., February 16, 2006.URL http://nonabelian.com/754/

RNDGMODE.TXT.

Kahan:2006:TSS

[289] W. Kahan. Is there a small skew Cay-ley transform with zero diagonal? Lin-ear Algebra and its Applications, 417(2–3):335–341, 2006. CODEN LAAPAW.

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Boldo:2007:PCA

[290] Sylvie Boldo, Marc Daumas, WilliamKahan, and Guillaume Melquiond.Proof and certification of an accuratediscriminant. In Luther and Otten[327], page ?? ISBN 0-7695-2821-X.LCCN QA297.I5 2007. URL http://

ieeexplore.ieee.org/servlet/opac?

punumber=4402381. IEEE ComputerSociety Order Number E2821.

Demmel:2007:PNL

[291] James W. Demmel, Jack J. Don-garra, Beresford N. Parlett, WilliamKahan, Ming Gu, David S. Bindel,Yozo Hida, Xiaoye S. Li, Osni A. Mar-ques, E. Jason Riedy, Christof Vomel,Julien Langou, Piotr Luszczek, JakubKurzak, Alfredo Buttari, Julie Lan-gou, and Stanimire Tomov. Prospec-tus for the next LAPACK and ScaLA-PACK libraries. LAPACK WorkingNote 181, Department of Computer Sci-ence, University of Tennessee, Knoxville,Knoxville, TN 37996, USA, March 11,2007. URL http://www.netlib.org/

lapack/lawnspdf/lawn181.pdf.

Kahan:2007:WCD

[292] William Kahan. Why I can debug someprograms and you can’t. In Du et al.[326], page ?? ISBN ???? LCCN???? URL http://www.stanford.edu/

group/compmath50/docs/CompMath50Pgm21.

pdf.

Kahan:2008:BFU

[293] William Kahan. Back to the future ofundebuggable floating-point computa-tion in science and engineering. Web

document, March 30, 2008. URLhttp://math.berkeley.edu/bascd08;

http://www.eecs.berkeley.edu/~

wkahan/BASCD08K.pdf. The Bay AreaScientific Computing Day, BASCD08,honoring Profs. Kahan and Parlett, 29–30 March, 2008.

Li:2012:FAN

[294] Ren-Cang Li and William Kahan. Afamily of Anadromic numerical meth-ods for matrix Riccati differential equa-tions. Mathematics of Computation, 81(277):233–265, ???? 2012. CODENMCMPAF. ISSN 0025-5718 (print),1088-6842 (electronic). URL http:

//www.ams.org/journals/mcom/2012-

81-277/S0025-5718-2011-02498-1;

http://www.ams.org/journals/mcom/

2012-81-277/S0025-5718-2011-02498-

1/S0025-5718-2011-02498-1.pdf.

Rubio-Gonzalez:2013:PTA

[295] Cindy Rubio-Gonzalez, Cuong Nguyen,Hong Diep Nguyen, James Demmel,William Kahan, Koushik Sen, David H.Bailey, Costin Iancu, and David Hough.Precimonious: Tuning assistant forfloating-point precision. In Proceed-ings of the International Conference onHigh Performance Computing, Network-ing, Storage and Analysis, page 27.ACM Press, New York, NY 10036, USA,2013.

Kahan:2015:ATP

[296] W. Kahan. Accuracy tests for poly-nomials’ zero-finders. Report, Depart-ment of Mathematics and Departmentof Electrical Engineering and Com-puter Science, University of California,Berkeley, Berkeley, CA, USA, Septem-ber 13, 2015. 17 pp. URL http:

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//www.eecs.berkeley.edu/~wkahan/

Math128/Fibs_2_6.pdf.

Kahan:2015:EBZ

[297] W. Kahan. Error-bounds for a zero ofa polynomial. Report, Department ofMathematics and Department of Elec-trical Engineering and Computer Sci-ence, University of California, Berkeley,Berkeley, CA, USA, October 30, 2015. 6pp. URL http://www.eecs.berkeley.

edu/~wkahan/Math128/PolyZbnd.pdf.

Gustafson:2016:TGD

[298] John Gustafson and William Kahan.Transcription of “the great debate”:John Gustafson vs. William Kahan onunum arithmetic. Web document.,July 12, 2016. URL http://www.

johngustafson.net/pdfs/DebateTranscription.

pdf.

Kahan:2016:CEE

[299] W. Kahan. Commentary on The End ofError — Unum Computing, by John L.Gustafson, (2015) CRC Press. Report,Department of Mathematics and De-partment of Electrical Engineering andComputer Science, University of Cali-fornia, Berkeley, Berkeley, CA, USA,July 15, 2016. 39 pp. URL https://

people.eecs.berkeley.edu/~wkahan/

EndErErs.pdf.

Kahan:2016:KO

[300] W. Kahan. Keplerian orbits. Report,Department of Mathematics and De-partment of Electrical Engineering andComputer Science, University of Cali-fornia, Berkeley, Berkeley, CA, USA,June 21, 2016. 2 pp. URL http:

//www.eecs.berkeley.edu/~wkahan/

Math128/KeplerOrbits.pdf.

Rubio-Gonzalez:2016:FPP

[301] Cindy Rubio-Gonzalez, Cuong Nguyen,Benjamin Mehne, Koushik Sen, JamesDemmel, William Kahan, Costin Iancu,Wim Lavrijsen, David H. Bailey, andDavid Hough. Floating-point precisiontuning using blame analysis. In Pro-ceedings of the 38th International Con-ference on Software Engineering, pages1074–1085. ACM Press, New York, NY10036, USA, 2016.

Kahan:2018:TD

[302] William Kahan. The tanpi dilemma.Web document., April 16, 2018. URLhttp://754r.ucbtest.org/background/

tanpi.txt; http://www.math.utah.

edu/pub/tex/bib/elefunt.bib.

Bunch:1995:EDB

[303] James R. Bunch. Editorial: Dedicatedto Beresford Parlett and William Kahan.Numerical Linear Algebra with Applica-tions, 2(2):85, 1995. CODEN NLAAEM.ISSN 1070-5325 (print), 1099-1506 (elec-tronic).

Boldo:2009:KAC

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Documents

A Bibliography of Publications of William M. Kahan fileA Bibliography of Publications of William M. Kahan Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155