Accuracy and Stability of Numerical Algorithms: Second EditionSIAM, 1 janv. 2002 - 710 pages Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior 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. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. 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. |
Table des matières
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 |
Autres éditions - Tout afficher
Accuracy and Stability of Numerical Algorithms: Second Edition Nicholas J. Higham Aperçu limité - 2002 |
Accuracy and Stability of Numerical Algorithms: Second Edition Nicholas J. Higham Aucun aperçu disponible - 2002 |
Expressions et termes fréquents
accuracy algorithm Anal Appl applied approximation arithmetic assume backward error block chapter column complete componentwise computed condition number consider constant convergence defined derived described diagonal digits eigenvalues elements equality equation error analysis error bound estimate evaluation exact example first follows formula forward error function given gives growth Hence Higham holds Householder IEEE implementation inequality inverse 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 positive definite precision problem proof properties QR factorization References residual result rounding errors routines satisfies scaling shows SIAM singular Software solution solving square stability standard summation symmetric symmetric matrix Theorem triangular upper vector Wilkinson yields zero