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Numerical methods for roots of polynomials. Part I. (English) Zbl 1143.65002
Studies in Computational Mathematics 14. Amsterdam: Elsevier (ISBN 978-0-444-52729-5/hbk). xix, 333 p. p. EUR 119.70 (2007).

Publisher’s description: This book (along with volume 2 covers most of the traditional methods for polynomial root-finding such as Newton’s, as well as numerous variations on them invented in the last few decades. Perhaps more importantly it covers recent developments such as Vincent’s method, simultaneous iterations, and matrix methods. There is an extensive chapter on evaluation of polynomials, including parallel methods and errors. There are pointers to robust and efficient programs. In short, it could be entitled “A Handbook of Methods for Polynomial Root-finding”. This book will be invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic.

Table of Contents: Preface; Contents; Introduction; 1. Evaluation, Convergence, Bounds; 2. Sturm Sequences and Greatest Common Divisors; 3. Real Roots by Continued Fractions; 4. Simultaneous Methods; 5. Newton’s and Related Methods; 6. Matrix Models; Index.

65-01Textbooks (numerical analysis)