Accuracy and Stability of Numerical Algorithms (2nd Revised edition)
By: Nicholas J. Higham (author)Hardback
1 - 2 weeks availability
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.
Preface; 1. Principles of finite precision computation; 2. Floating point arithmetic; 3. Basics; 4. Summation; 5. Polynomials; 6. Norms; 7. Perturbation theory for linear systems; 8. Triangular systems; 9. LU factorization and linear equations; 10. Cholesky factorization; 11. Symmetric indefinite and skew-symmetric systems; 12. Iterative refinement; 13. Block LU factorization; 14. Matrix inversion; 15. Condition number estimation; 16. The Sylvester equation; 17. Stationary iterative methods; 18. Matrix powers; 19. QR factorization; 20. The least squares problem; 21. Underdetermined systems; 22. Vandermonde systems; 23. Fast matrix multiplication; 24. The fast Fourier transform and applications; 25. Nonlinear systems and Newton's method; 26. Automatic error analysis; 27. Software issues in floating point arithmetic; 28. A gallery of test matrices; Appendices; Bibliography; Name index; Subject index.
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- ID: 9780898715217
2nd Revised edition
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