Iterative Methods for Simultaneous Inclusion of Polynomial Zeros

1. Front Matter

   Pages I-X

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2. Introduction

   • Miodrag Petković

   Pages 1-9

3. Basic concepts

   • Miodrag Petković

   Pages 10-30

4. Iterative methods without derivatives

   • Miodrag Petković

   Pages 31-68

5. Generalized root iterations

   • Miodrag Petković

   Pages 69-162

6. Bell's polynomials and parallel disk iterations

   • Miodrag Petković

   Pages 163-220

7. Computational efficiency of simultaneous methods

   • Miodrag Petković

   Pages 221-249

8. Back Matter

   Pages 250-263

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The simultaneous inclusion of polynomial complex zeros is a crucial problem in numerical analysis. Rapidly converging algorithms are presented in these notes, including convergence analysis in terms of circular regions, and in complex arithmetic. Parallel circular iterations, where the approximations to the zeros have the form of circular regions containing these zeros, are efficient because they also provide error estimates. There are at present no book publications on this topic and one of the aims of this book is to collect most of the algorithms produced in the last 15 years. To decrease the high computational cost of interval methods, several effective iterative processes for the simultaneous inclusion of polynomial zeros which combine the efficiency of ordinary floating-point arithmetic with the accuracy control that may be obtained by the interval methods, are set down, and their computational efficiency is described. The rate of these methods is of interest in designing a package for the simultaneous approximation of polynomial zeros, where automatic procedure selection is desired. The book is both a text and a reference source for mathematicans, engineers, physicists and computer scientists who are interested in new developments and applications, but the material is also accessible to anyone with graduate level mathematical background and some knowledge of basic computational complex analysis and programming.

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