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Accuracy and stability of numerical algorithms. 2nd ed. (English) Zbl 1011.65010
Philadelphia, PA: SIAM. xxx, 680 p. (2002).
For a review of the original ed. (SIAM 1996) see Zbl 0847.65010.
The text is centered around accuracy and stability for the solution of systems of linear equations. It is dedicated to the pioneers in this field, Alan Turing and James Wilkinson. The present edition contains several additions and refinements.
After 5 chapters on basic procedures with floating point arithmetic and a chapter on polynomials the author turns to the solution of linear equations by Gaussian elimination and its variants and some stationary iterative methods. In the second edition a chapter on nonlinear systems and Newton’s method is added. The book concludes with information on software and library packages and gallery of test matrices. The Appendix with solutions to the problems covers 50 pages.
The chapters contain sections about solution methods, perturbation theory, error analysis, problems, and the usage of the LAPACK package. Besides the theorems with and without proofs there are many notes including those on historical perspectives. All items are accompanied by well-collected references that sum up to a bibliography with 1287 entries. This are 153 more entries than in the first edition.
As often, a book becomes also interesting by topics that are beyond the main stream. We mention the fast multiplication of matrices by Winograd and Strassen or block LDL\(^T\) factorization for skew-symmetric matrices. A pleasure are also the quotations at the start of each chapter, which are an art gallery of numerical facts, names, and curiosities.

65Fxx Numerical linear algebra
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
65G50 Roundoff error
15-04 Software, source code, etc. for problems pertaining to linear algebra
LAPACK; mctoolbox
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