Accuracy and Stability of Numerical Algorithms

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.

Nicholas J. Higham is Richardson Professor of Applied Mathematics at the University of Manchester, England. He is the author of more than 80 publications and is a member of the editorial boards of Foundations of Computational Mathematics, the IMA Journal of Numerical Analysis, Linear Algebra and Its Applications, and the SIAM Journal on Matrix Analysis and Applications. His book Handbook of Writing for the Mathematical Sciences (second edition) was published by SIAM in 1998, and his book MATLAB Guide, co-authored with Desmond J. Higham, was published by SIAM in 2000.