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Overview
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.
Editorials
This graduate textbook deals with the effects of finite precision arithmetic on numerical algorithms, particularly the rounding errors that arise in numerical linear algebra. Higham (applied mathematics, University of Manchester) examines Gaussian elimination, LU and QR factorization, and the least squares problem, among others. The second edition adds chapters on symmetric indefinite and skew-symmetric systems, and nonlinear systems and Newton's method. Annotation c. Book News, Inc., Portland, OR
Booknews
Treats the behavior of numerical algorithms in finite precision arithmetic, combining algorithmic derivations, perturbation theory, and rounding error analysis and emphasizing software practicalities, with particular reference to LAPACK and MATLAB. Includes historical perspectives, especially on the work of Wilkinson and Turing, with quotations introducing chapters on subjects such as floating point summation, condition number estimation, and the Sylvester equation. Although designed as a reference rather than a text, it includes problems and solutions. Annotation c. Book News, Inc., Portland, OR (booknews.com)Jaroslav Stark
An attempt (successful in my opinion) to produce a successor to Wilkinson's text and give both a modern treatment of the material presented there, and to give a comprehensive account of the many developments in the subject since Wilkinson's time. .I thoroughly recommend the volume to anyone who uses computers in their work.— Mathematics Today
S. Hitotumatu
This book is a monumental work on the analysis of rounding error and will serve as a new standard textbook on this subject, especially for linear computation.— Mathematical Reviews
S. Siltanen
A comprehensive book concerning linear algebraic calculations with floating-point arithmetic. In its successful effort to give deep understanding of finite precision computations spiced with historical aspects, the book honors its classical predecessors, namely Wilkinson's books. .The nearly 700 pages.are written in a lively and down-to-earth manner, keeping several aspects in mind all the time: algorithmic derivations, perturbation theory, and rounding error analysis. Well organized material combined with up-to-date examples, a bibliography with more than 1000 entries, and a collection of good exercises constitutes a convincing piece of scientific literature.— Inverse Problems