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Frontiers in Mathematics

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

Authors: Ezquerro, Jose A, Hernández Verón, Miguel Angel

  • Up-to-date account of Kantorovich´s theory for Newton´s method
  • Starts with a detailed presentation of Kantorovich´s approach and ends with new results and alternative approaches
  • Contains many numerical examples involving nonlinear integral equations
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eBook $54.99
price for USA (gross)
  • ISBN 978-3-319-55976-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-319-55975-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

About the authors

José Antonio Ezquerro is Professor at the Department of Mathematics and Computation at the University of La Rioja in Spain.
M. A. Hernández-Verón is Professor at the Department of Mathematics and Computation at the University of La Rioja in Spain. 

Table of contents (4 chapters)

  • The classic theory of Kantorovich

    Ezquerro Fernández, José Antonio (et al.)

    Pages 1-38

  • Convergence conditions on the second derivative of the operator

    Ezquerro Fernández, José Antonio (et al.)

    Pages 39-81

  • Convergence conditions on the k-th derivative of the operator

    Ezquerro Fernández, José Antonio (et al.)

    Pages 83-125

  • Convergence conditions on the first derivative of the operator

    Ezquerro Fernández, José Antonio (et al.)

    Pages 127-159

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-319-55976-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-319-55975-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Newton’s Method: an Updated Approach of Kantorovich’s Theory
Authors
Series Title
Frontiers in Mathematics
Copyright
2017
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-55976-6
DOI
10.1007/978-3-319-55976-6
Softcover ISBN
978-3-319-55975-9
Series ISSN
1660-8046
Edition Number
1
Number of Pages
XII, 166
Number of Illustrations and Tables
19 illustrations in colour
Topics