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Point Estimation of Root Finding Methods

  • Miodrag Petković

Part of the Lecture Notes in Mathematics book series (LNM, volume 1933)

Table of contents

About this book

Introduction

This book sets out to state computationally verifiable initial conditions for predicting the immediate appearance of the guaranteed and fast convergence of iterative root finding methods. Attention is paid to iterative methods for simultaneous determination of polynomial zeros in the spirit of Smale's point estimation theory, introduced in 1986. Some basic concepts and Smale's theory for Newton's method, together with its modifications and higher-order methods, are presented in the first two chapters. The remaining chapters contain the recent author's results on initial conditions guaranteing convergence of a wide class of iterative methods for solving algebraic equations.

These conditions are of practical interest since they depend only on available data, the information of a function whose zeros are sought and initial approximations. The convergence approach presented can be applied in designing a package for the simultaneous approximation of polynomial zeros.

Keywords

Newton's method guaranteed convergence iterative root finders point estimation polynomial zeros solving nonlinear equations

Editors and affiliations

  • Miodrag Petković
    • 1
  1. 1.Department of Mathematics Faculty of Electronic EngineeringUniversity of NišNišSerbia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-77851-6
  • Copyright Information Springer Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-77850-9
  • Online ISBN 978-3-540-77851-6
  • Series Print ISSN 0075-8434
  • Buy this book on publisher's site