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Higham N. Ч Accuracy and stability of numerical algorithms
Higham N. Ч Accuracy and stability of numerical algorithms



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Ќазвание: Accuracy and stability of numerical algorithms

јвтор: Higham N.

јннотаци€:

Treats the behavior of numerical algorithms in finite precision arithmetic, combining algorithmic derivations, perturbation theory, and rounding error analysis and emphasizing software practicalities, with particular reference to LAPACK and MATLAB. Includes historical perspectives, especially on the work of Wilkinson and Turing, with quotations introducing chapters on subjects such as floating point summation, condition number estimation, and the Sylvester equation. Although designed as a reference rather than a text, it includes problems and solutions. Annotation c. by Book News, Inc., Portland, Or.


язык: en

–убрика: ћатематика/„исленные методы/„исленный анализ/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1996

 оличество страниц: 688

ƒобавлена в каталог: 23.02.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Raimi, Ralph A.      52
Ramos, George U.      470
Random matrices      517Ч520
Random matrices with given singular values      519Ч520
Random matrices, 2-norm of      518
Random matrices, condition number of      518
Random matrices, expected number of real eigenvalues      518
Random matrices, orthogonal      519 527
Random matrices, spectral radius of      518
Random matrices, tend to be well conditioned      518
Randsvd matrix      519Ч520 527
Range reduction      54
Rath, Wolfgang      385
Ratz, Deitmar      487
Ratz, H. C      327
Razaz, M.      113
RCOND condition estimator (UNPACK, MATLAB)      305 480Ч481 489
Reichel, Lothar      113 358 440Ч442 527
Reichelt, Mark W.      527
Reid, J. K      3 190 193 197 200 226 411
Reinsch, C.      xxviii 284 585
Reiser, John F.      58
Relative error      4 5
Relative error counter, <k>      75
Relative error, componentwise      5
Relative precision      76
Relative residual      14
Ren, Huan      60
Research problems      102 115 201 229 244 287 308 324 359 423 442 463 490 527 528
Residual, relative      14
Rew, R. K.      289q 299 480
Riccati equation, algebraic      322
Rice, John R.      33 385
Richtmyer, Robert D.      32
Rigal Ч Gaches backward error theorem      132
Rigal, J. L.      132 145
Robertazzi, T. G.      98
Roberts, J. D.      322
Rohn, Jiri      128 140 141 149
Romani, Francesco      328
Rose, Donald J.      257
Rosenthal, Peter      322
Ross, D. R.      97
Rounding      4 42
Rounding error analysis, automatic      473Ч490
Rounding error analysis, demystified      82Ч83
Rounding error analysis, graphs in      83
Rounding error analysis, model with underflow      61
Rounding error analysis, model without guard digit      49
Rounding error analysis, model, standard      44
Rounding error analysis, notation      73Ч76
Rounding error analysis, ordering of operations, effect of      77 154
Rounding error analysis, purpose of      71Ч72 203q
Rounding error analysis, statistical approach      52Ч53
Rounding errors are not random      29 52
Rounding errors in subtraction      49Ч50
Rounding errors, accumulation of      16
Rounding errors, beneficial effects of      26Ч27
Rounding errors, cancellation of      21Ч26
Rounding errors, statistical assumptions on      52Ч53
Rounding to even versus to odd      58
Rounding, dealing with ties      42 58
Rowan, Thomas Harvey      488 489
Rubin, Donald B.      391q 410
Ruhe, Axel      385
Ruiz, Daniel      343
Rules of thumb, condition for computed powers of matrix to converge to zero      358
Rules of thumb, forward error related to backward error and condition number      10
Rules of thumb, relative speed of floating point operations      60
Rules of thumb, square root of constants in error bound      52
Runge Ч Kutta method      92 100
Running error analysis      73 489
Running error analysis for continued fraction      85
Running error analysis for HomerТs method      105Ч106 113
Running error analysis for inner product      72Ч73
Rust, B. W.      145
Rutishauser, Heinz      514 520
Sameh, Ahmed H.      162 164 488
Samelson, Klaus      57
Sample variance      see УVarianceФ
Sande, G.      470
Sanz-Serna, J. M.      32 33
Saunders, Michael A.      225 226 229 257 422
Sautter, Werner      190
Scalapack      588
Scaling a linear system before Gaussian elimination      191Ч192 197Ч198
Scaling to minimize the condition number      136Ч139 191
Scarborough, James B.      33 58
Schaumburg, Kjeld      305
Schelin, Charles W.      61
Scherer, R.      84
Schnabel, Robert B.      32
Schneider, Hans      124 359
Schonfelder, J. L.      113
Schreiber, Robert S.      165 180 245q 250Ч253 257 371 384 576
Schryer, N. L.      498
Schur complement      219 224 247 252
Schur complement, perturbation bounds for symmetric positive semidefinite matrix      212Ч218
Schwartz, S. C      98
Schwetlick, Hubert      84 406 411 418 422
Searle, Shayle R.      323 490
Second difference matrix      525
Semiconvergent matrix      337
Seminormal equations for least squares problem      403Ч404
Seminormal equations for underdetermined system      417
Separation (sep), of two matrices      318
Sha, Xuan-He      450 459
Shampine, Lawrence F.      32 33 84 95 527
Shannon, Claude E.      60
Shapiro, Alexander      146
Shepherd, David      59
Sherman Ч Morrison formula      197 490
Shinnerl, Joseph R.      225 229
Shroff, Gautam M.      301
Shub, Michael      147 518
Significance arithmetic      489
Significant digits, correct      4Ч5 32
Significant digits, least and most significant      40
Simon, Horst D.      460
Singular value decomposition (SVD)      580
Skeel, Robert D.      36 135 146 190 192 198 235 240 241 486
Slishman, Gordon      460 575
Smale, Steve      2n
Smith, David M.      505
Smith, Francis J.      113 439
Smith, Jon M.      37
Smith, Robert L.      503 509
Smith, Roger M.      460 575
Smoktunowicz, Alicja      94 141 149 242
Snyder, James N.      231q 241
Software, avoiding underflow and overflow      502Ч504
Software, effects of underflow      504
Software, issues in floating point arithmetic      491Ч512
Software, portability      499Ч502
Software, specifying arithmetic parameters      499Ч500
Software, specifying numerical constants      501
Sokolnicka, Jolanta      242
SOR method, forward error analysis      334
Sorensen, Danny C      195 225 229 257
Sorevik, T.      461
Spellucci, P.      32
Spencer, Herbert      665
Spieb, J.      460
Spooner, David      488
Square root, of complex number      36
Stable algorithms, designing      30Ч31
Stationary iterative methods      325Ч343
Stationary iterative methods and powers of a matrix      358
Stationary iterative methods, backward error analysis      334Ч336
Stationary iterative methods, forward error analysis      329Ч334
Stationary iterative methods, forward error analysis, singular systems      338Ч341
Stationary iterative methods, Jacobi method      332Ч334
Stationary iterative methods, scale independence      331
Stationary iterative methods, singular systems, theory for      336Ч338
Stationary iterative methods, SOR      334
Stationary iterative methods, stopping criteria      341Ч342
Statistics      34 (see also УVariance computational referencesФ)
Steele, Jr., Guy L.      61
Steer, J.      83 84 119 126 127 190
Stegun, Irene A.      35
Sterbenz, Pat H.      33 34 50 57 60 489
Stewart, G W. (Pete)      xxiv 75 113 119 126 131q 139 146 147 151q 164 174 195 197 198 224 231q 241 242 297 305 312 324 359 381 382 385 386 392 394 407 504 519 527 580
Stewart, William J.      305
Sticky bit      46
Stone, Betty Jane      126
Storey, C      323
Stoutemyer, David R.      489
Strakos, Zdenek      329
Strang, Gilbert      15 124 146 471
Strassen, Volker      446 461 462
StrassenТs method      446Ч448
StrassenТs method for inversion      461Ч462 481Ч482
StrassenТs method, accuracy compared with conventional multiplication      454Ч455
StrassenТs method, error analysis      452Ч456
StrassenТs method, error versus operation count      16
StrassenТs method, implementation issues      460
StrassenТs method, WinogradТs variant      448 455Ч456
Straus, E. G      138 146
Street, Anne Penfold      179
Stummel, Friedrich      34 83 191
Subdifferential, of a vector norm      291
Subgradient      292
Subnormal numbers      41 47 495
Summation      87Ч102
Summation, choice of method: summary      98Ч100
Summation, compensated and applications      92Ч97
Summation, condition number      100
Summation, criterion for minimizing error      90
Summation, distillation algorithms      98
Summation, doubly compensated      96Ч97
Summation, error analysis      89Ч92
Summation, insertion method      88
Summation, pairwise (fan-in)      88
Summation, recursive      88
Summation, recursive, ordering in      19 90Ч91
Summation, statistical error estimates      98
Sun, Ji-guang      119 126 131q 139 146 194 198 209 224 382 386 392 394 404 407 409 411 413 580
Sun, Xiaobai      384
SVD (singular value decomposition)      580
Swarm, W. H.      474
Swartzlander, Jr., Earl E.      54
Sweeney, D. W.      60
Swenson, J. R.      52
Sylvester equation      309Ч324
Sylvester equation, backward error      313Ч316
Sylvester equation, Bartels Ч Stewart method      311Ч313
Sylvester equation, generalizations      321Ч324
Sylvester equation, perturbation theory      318Ч320
Sylvester equation, practical error bounds      320Ч321
Sylvester equation, solution methods      311Ч313
Sylvester, James Joseph      309q 322 446
Symbolic manipulation package      6
Symmetric indefinite factorization      218 (see also УDiagonal pivoting methodФ)
Symmetric indefinite matrix      218
Symmetric positive definite matrix      204
Symmetric positive definite matrix and block LU factorization      255Ч257
Symmetric positive definite matrix, practical test for      225
Symmetric positive semidefinite matrix      210
Symmetric positive semidefinite matrix, determinantal conditions for      228
Symmetric quasidefinite matrix      229
Synthetic division      107
TablemakerТ s dilemma      5
Tang, Ping Tak Peterj      61 499 530
Tang, W. P.      441
Tao, Pham Dinh      128 304
Tartaglia, Niccolo      483
Taussky, Olga      513q 515
Test for accuracy of floating point arithmetic      54Ч56
Test for guard digit      56
Test matrices      513Ч528
Test matrices, Harwell Ч Boeing collection      527
Test matrices, Test Matrix Toolbox      591Ч594
Teukolsky, Saul A.      479 490 507
Thacher, Jr., Henry C      196
Thisted, Ronald A.      34
Thompson, Sir DТarcy Wentworth      1q
Thron, W. J.      507
Tienari, Martti      53
Todd, John      126 514 520 526 527
Toeplitz matrix, pseudospectra      527 528
Toeplitz matrix, tridiagonal      524Ч525
Toh, Kim-Chuan      483n 526
Torczon, Virginia J.      477Ч479
Tornheim, L.      180 181
Totally nonnegative matrix      176 523
Totally nonnegative matrix, LU factorization      176 196
Totally nonnegative matrix, LU factorization, row scaling in      192
Totally nonnegative matrix, test for      196
Trammer, Manfred R.      32 346 355 358
Transformations, well conditioned      30
Transputer (Inmos), proof of arithmeticТs correctness      59
Traub, J. F.      440
Trefethen, Lloyd N.      6q 32 169q 180 328 345q 346 348 352 353 355 358 483n 526 527
Tremaine, Scott      96
Triangular matrix, bounds for inverse      159Ч161
Triangular matrix, condition numbers      155
Triangular matrix, inversion      265Ч270
Triangular matrix, inversion methods, blocked      267Ч270
Triangular matrix, inversion methods, unblocked      265Ч267
Triangular matrix, M-matrix      157 159 160
Triangular systems      151Ч168
Triangular systems, accurate solution of      151q 155 156 159
Triangular systems, conditioning      156Ч157
Triangular systems, fan-in algorithm      162Ч164
Triangular systems, partitioned inverse method      165
Triangular systems, substitution, backward error analysis      152Ч154
Triangular systems, substitution, forward error analysis      155Ч159
Tridiagonal matrix      183Ч186
Tridiagonal matrix, condition number estimation      301Ч303
Tridiagonal matrix, growth factor      183
Tridiagonal matrix, LU factorization      184
Tridiagonal matrix, LU factorization, error analysis of      184Ч186
Tridiagonal matrix, structure of inverse      303 305
Tridiagonal matrix, Toeplitz      524Ч525
Tropp, Henry S.      491n
Truncation error      6
Tsao, Nai-kuan      84 384
Tukey, John W.      60 470
Turing Award of the ACM      xxvii 59
Turing programming language      506
Turing programming language, Numerical Turing      506
Turing, Alan Mathison      xxvii xxviii 33 126 131q 188 284 485
Turing, Alan Mathison, contributions in 1948 paper "Rounding-off errors..."      188 284
Turnbull, H. W.      383 523
Turner, Kathryn      225
Turner, Peter R.      51 53 165
Tyrtyshnikov, Evgenij E.      526
Ulp (unit in last place)      43
Uncertainty, in data      5
Underdetermined system      415Ч423
Underdetermined system, backward error      419 423
Underdetermined system, backward stability, definition      419
Underdetermined system, error analysis      421
Underdetermined system, modified Gram Ч Schmidt      421Ч422
Underdetermined system, perturbation theory      417Ч419
Underdetermined system, Q method (QR factorization)      416
Underdetermined system, Q method (QR factorization), error analysis      419Ч422
Underdetermined system, seminormal equations      417
Underflow      18 42
Underflow, avoiding      502Ч504
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