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Newton’s Method: an Updated Approach of Kantorovich’s Theory

  • José Antonio Ezquerro Fernández
  • Miguel Ángel Hernández Verón

Part of the Frontiers in Mathematics book series (FM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. José Antonio Ezquerro Fernández, Miguel Ángel Hernández Verón
    Pages 1-38
  3. José Antonio Ezquerro Fernández, Miguel Ángel Hernández Verón
    Pages 39-81
  4. José Antonio Ezquerro Fernández, Miguel Ángel Hernández Verón
    Pages 83-125
  5. José Antonio Ezquerro Fernández, Miguel Ángel Hernández Verón
    Pages 127-159
  6. Back Matter
    Pages 161-166

About this book

Introduction

This book shows the importance of studying semilocal convergence in iterative methods through Newton's method and addresses the most important aspects of the Kantorovich's theory including implicated studies. Kantorovich's theory for Newton's method used techniques of functional analysis to prove the semilocal convergence of the method by means of the well-known majorant principle. To gain a deeper understanding of these techniques the authors return to the beginning and present a deep-detailed approach of Kantorovich's theory for Newton's method, where they include old results, for a historical perspective and for comparisons with new results, refine old results, and prove their most relevant results, where alternative approaches leading to new sufficient semilocal convergence criteria for Newton's method are given. The book contains many numerical examples involving nonlinear integral equations, two boundary value problems and systems of nonlinear equations related to numerous physical phenomena. The book is addressed to researchers in computational sciences, in general, and in approximation of solutions of nonlinear problems, in particular.

Keywords

Newton’s Method Kantorovich’s Theory Semilocal Convergence Majorizing Sequence Error Estimates Order of Convergence

Authors and affiliations

  • José Antonio Ezquerro Fernández
    • 1
  • Miguel Ángel Hernández Verón
    • 2
  1. 1.University of La Rioja Department of Mathematics and ComputationLa RiojaSpain
  2. 2.Dept. de Matemáticas y ComputaciónUniversidad de La Rioja Dept. de Matemáticas y ComputaciónLogroñoSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-55976-6
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-55975-9
  • Online ISBN 978-3-319-55976-6
  • Series Print ISSN 1660-8046
  • Series Online ISSN 1660-8054
  • Buy this book on publisher's site