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Iterative Methods for Simultaneous Inclusion of Polynomial Zeros

  • Book
  • © 1989
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Overview

Authors:
  1. Miodrag Petković
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1387)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Miodrag Petković
    Pages 1-9
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  3. Basic concepts

    • Miodrag Petković
    Pages 10-30
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  4. Iterative methods without derivatives

    • Miodrag Petković
    Pages 31-68
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  5. Generalized root iterations

    • Miodrag Petković
    Pages 69-162
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  6. Bell's polynomials and parallel disk iterations

    • Miodrag Petković
    Pages 163-220
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  7. Computational efficiency of simultaneous methods

    • Miodrag Petković
    Pages 221-249
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  8. Back Matter

    Pages 250-263
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Iterative Methods for Simultaneous Inclusion of Polynomial Zeros

  • Authors: Miodrag Petković

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0083599

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • Softcover ISBN: 978-3-540-51485-5Published: 09 August 1989

  • eBook ISBN: 978-3-540-48174-4Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 268

  • Topics: Numerical Analysis

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