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Higham N. — Accuracy and stability of numerical algorithms
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Название: Accuracy and stability of numerical algorithmsАвтор: Higham N. Аннотация: 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: Рубрика: Математика /Численные методы /Численный анализ /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1996Количество страниц: 688Добавлена в каталог: 23.02.2005Операции: Положить на полку |
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Underflow, effects on software 504 Underflow, model for error analysis 61 Underhill, L. G. 527 Ungar, Peter 461 UNICOS library (Cray) 448 450 Unit roundoff 3 42 Update formula, involving small correction 30 Urabe, Minora 62 Uspensky, J. V. 490 Vajtersic, M. 461 van der Sluis, A. 137 138 198 207 391q 409 Van der Sluis’s theorem 137 Van der Vorst, Henk A. 195 225 257 329 Van Loan, Charles F. xxiv 27 141 149 182 190 195 223 225 229 231q 257 299 311 312 312n 345q 348 352 359 370 371 384 386 388 392 409 412 465q 466 470 580 van Veldhuizen, M. 196 van Wijngaarden, A. 501 Vancouver Stock Exchange, inaccurate index 57—58 Vanderbei, Robert J. 229 Vandermonde matrix, bounds and estimates for condition number 428 Vandermonde matrix, definition 426 Vandermonde matrix, inverse 426—428 Vandermonde matrix, inversion algorithm 427 Vandermonde matrix, LU factorization in factored form 432—433 Vandermonde matrix, QR factorization 441 Vandermonde matrix, structured condition number 440—441 Vandermonde system 425—443 Vandermonde system, accuracy independent of condition number 436 Vandermonde system, algorithm for dual 431—432 Vandermonde system, algorithm for primal 433—434 Vandermonde system, algorithm for residual of confluent system 439 Vandermonde system, backward error analysis 437 Vandermonde system, complexity results 441 Vandermonde system, curing instability 438—440 Vandermonde system, forward error analysis 435—436 Vandermonde system, history of solution methods 441 Vandermonde system, preventing instability 438 Vandermonde-like matrix, confluent, definition 429 Vandermonde-like matrix, definition 429 Vandermonde-like matrix, determinant 442 Varah, James M. 146 167 257 258 Varga, Richard S. 160 167 257 508 Variance, algorithms for computing 12—13 33 Variance, condition numbers for 37 Variance, error bound for two-pass formula 38 Vec operator 310 Vemulapati, Udaya B. 301 412 Venus probe, loss due to program bug 491q Veselic, Kresimir 225 Vet-permutation matrix 319 323 Vetterling, William T. 479 490 507 Vieta, Franciscus 483 Vignes, J. 53 Vitasek, Emil 100 Viten’ko, I. V. 95 von Neumann, John 33 52 186 187 196 263 517 Waite, William 497 499 Walden, Bertil 404 413 Walker, Homer R. 32 328 Wallis, Jennifer Seberry 179 Wallis, W. D. 179 Wang, Johnson J. H. 198 Ward, Robert C. 285 Warming, Robert F. 527 Wasilkowski, G. W. 147 Wasniewski, Jerzy 305 Wasow, Wolfgang R. 32 Watson, G. A. 146 Watterson, Bill 473 Wedderburn, J. H. M. 117q Wedin, Per-Ake 392 407 409 412 422 Wedin’s least squares perturbation theorem 392—393 Wedin’s least squares perturbation theorem, proof 407—409 Wegert, Elias 353 Wei, Musheng 388 410 Weidner Peter 486 Weiss, N. 147 Wendroff, Burton 189 197 Werner, Wilhelm 113 Westin, Lars 305 323 Westlake, Joan R. 514 Wette, Matthew R. 323 White, Jon L. 61 Wichmann, B. A. 499 502 Wilkinson, first program for Gaussian elimination 195—196 Wilkinson, J. H. xxi xxiv xxvii xxviii 14 25 31 33 34 39q 52 56 58 67q 73 75 84 100 103q 104 113 117q 145 151q 164 175 177 178 180—182 187—191 195—197 203q 207 208 224 232 241 252 279 283—285 287 297 326 327 343q 348 361q 364 365 384 385 387 391 400 409—411 474 485 542 585q Wilkinson, on the purpose of a priori error analysis 203q Wilkinson, solving linear systems on desk calculator in 1940s 187—188 Wilkinson, user participation in a computation 31 Williams, Jack 425q Wilson, Greg 60 Winograd, Shmuel 446 448 461 Winograd’s method 446 461 Winograd’s method, error analysis 451—452 Winograd’s method, scaling for stability 452 Wisniewski, John A. 488 Witzgall, C 119 126 127 Wobbling precision 43 51 Wolfe, Jack M. 97 Wolfe, Philip 32 Woodger, Michael 169q 445 Wozniakowski.H. 32 94 147 241 242 300 328 Wrathall, Celia 488 Wright, Margaret H. 32 225 479 Wright, Stephen J. 178 WY representation of product of Householder matrices 370—371 Yalamov, P. Y. 83 Yip, E. L. 490 Yohe, J. Michael 486 504 Yorke, James A. 32 Young, David M. 326t 350 Young, Gale 126 Yuvzd, Gideon 459 Zang, Thomas A. 32 Zawilski, Adam T. 328 Zehfuss, Johann Georg 323 Zeller, K. 84 Zeng, Z. 285 Zha, Hongyuan 167 382 Zielke, Gerhard 126 527 Zietak,K. 323 Ziv, Abraham 60 61 83 84 Zlatev, Zahari 305
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