E-Book Overview
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.
- First comprehensive treatment of Root-Finding in several decades. - Gives description of high-grade software and where it can be down-loaded. - Very up-to-date in mid-2006; long chapter on matrix methods. - Includes Parallel methods, errors where appropriate. - Invaluable for research or graduate course.
E-Book Content
Preface This book constitutes the first part of two volumes describing methods for finding roots of polynomials. In general most such methods are numerical (iterative), but one chapter in Part II will be devoted to “analytic” methods for polynomials of degree up to four. It is hoped that the series will be useful to anyone doing research into methods of solving polynomials (including the history of such methods), or who needs to solve many low- to medium-degree polynomials and/or some or many high-degree ones in an industrial or scientific context. Where appropriate, the location of good computer software for some of the best methods is pointed out. The book(s) will also be useful as a text for a graduate course in polynomial root-finding. Preferably the reader should have as pre-requisites at least an undergraduate course in Calculus and one in Linear Algebra (including matrix eigenvalues). T