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Iterative Methods for Simultaneous Inclusion of Polynomial Zeros

  • Authors
  • Miodrag Petković

Part of the Lecture Notes in Mathematics book series (LNM, volume 1387)

Table of contents

  1. Front Matter
    Pages I-X
  2. Miodrag Petković
    Pages 1-9
  3. Miodrag Petković
    Pages 10-30
  4. Miodrag Petković
    Pages 31-68
  5. Miodrag Petković
    Pages 69-162
  6. Miodrag Petković
    Pages 163-220
  7. Miodrag Petković
    Pages 221-249
  8. Back Matter
    Pages 250-263

About this book

Introduction

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.

Keywords

Mathematica Microsoft Access algorithms arithmetic complex analysis computation control convergence derivative efficiency iteration numerical analysis polynomial programming set

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0083599
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-51485-5
  • Online ISBN 978-3-540-48174-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site