Overview
- 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
Part of the book series: Frontiers in Mathematics (FM)
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Table of contents (4 chapters)
Keywords
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.
Reviews
“This book is well written and will be useful to researchers interested in the theory of Newton’s method in Banach spaces. Two of its merits have to be mentioned explicitly: the authors offer all details for the proofs of all the results presented in the book, and, moreover, they also include significant material from their own results on the theory of Newton's method which were carried out over many years of research work.” (Vasile Berinde, Mathematical Reviews, March, 2018)
Authors and Affiliations
About the authors
M. A. Hernández-Verón is Professor at the Department of Mathematics and Computation at the University of La Rioja in Spain.
Bibliographic Information
Book Title: Newton’s Method: an Updated Approach of Kantorovich’s Theory
Authors: José Antonio Ezquerro Fernández, Miguel Ángel Hernández Verón
Series Title: Frontiers in Mathematics
DOI: https://doi.org/10.1007/978-3-319-55976-6
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-55975-9Published: 14 July 2017
eBook ISBN: 978-3-319-55976-6Published: 05 July 2017
Series ISSN: 1660-8046
Series E-ISSN: 1660-8054
Edition Number: 1
Number of Pages: XII, 166
Number of Illustrations: 19 illustrations in colour
Topics: Operator Theory, Computational Mathematics and Numerical Analysis, Integral Equations