Accuracy and Stability of Numerical Algorithms: Second EditionSIAM, 01.08.2002 - 710 Seiten This book gives a thorough, up-to-date treatment of the behaviour of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. The coverage of the first edition has been expanded and updated, involving numerous improvements. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures. This new edition is a suitable reference for an advanced course and can also be used at all levels as a supplementary text from which to draw examples, historical perspective, statements of results, and exercises. In addition the thorough indexes and extensive, up-to-date bibliography are in a readily accessible form. |
Inhalt
OT80_ch1 | 1 |
OT80_ch2 | 35 |
OT80_ch3 | 61 |
OT80_ch4 | 79 |
OT80_ch5 | 93 |
OT80_ch6 | 105 |
OT80_ch7 | 119 |
OT80_ch8 | 139 |
OT80_ch18 | 339 |
OT80_ch19 | 353 |
OT80_ch20 | 381 |
OT80_ch21 | 407 |
OT80_ch22 | 415 |
OT80_ch23 | 433 |
OT80_ch24 | 451 |
OT80_ch25 | 459 |
OT80_ch9 | 157 |
OT80_ch10 | 195 |
OT80_ch11 | 213 |
OT80_ch12 | 231 |
OT80_ch13 | 245 |
OT80_ch14 | 259 |
OT80_ch15 | 287 |
OT80_ch16 | 305 |
OT80_ch17 | 321 |
OT80_ch26 | 471 |
OT80_ch27 | 489 |
OT80_ch28 | 511 |
OT80_appa | 527 |
OT80_appb | 573 |
OT80_appc | 577 |
OT80_appd | 583 |
OT80_bm | 587 |
Andere Ausgaben - Alle anzeigen
Accuracy and Stability of Numerical Algorithms: Second Edition Nicholas J. Higham Eingeschränkte Leseprobe - 2002 |
Accuracy and Stability of Numerical Algorithms: Second Edition Nicholas J. Higham Keine Leseprobe verfügbar - 2002 |
Häufige Begriffe und Wortgruppen
accuracy algorithm Anal Appl applied approximation arithmetic assume backward error block chapter Cholesky column complete componentwise computed condition number consider convergence defined derived described diagonal digits eigenvalues elements elimination equation error analysis error bound estimate evaluation exact example floating point arithmetic follows formula forward error function given gives growth Hence Higham holds Householder IEEE implementation inequality inverse ISBN iterative iterative refinement least Lemma Linear Algebra linear systems LU factorization machine Math Mathematics matrix method multiplication nonsingular norm normwise Note obtain operations partial pivoting perturbation pivoting polynomial positive definite precision problem proof QR factorization References residual result rounding errors satisfies scaling shows SIAM singular Software solution solving squares stability standard summation symmetric symmetric matrix Theorem triangular upper vector Wilkinson zero