This book provides a thorough, up-to-date treatment of the behaviour of numerical algorithms in finite precision arithmetic.

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.