Overview
- Presents a new iterative technique for solving nonlinear equations
- Substantially broadens the scope of Kantorovich’s theory for Newton’s method
- Intended for researchers and postgraduate students working on nonlinear equations
Part of the book series: Frontiers in Mathematics (FM)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
In this book the authors use a technique based on recurrence relations to study the convergence of the Newton method under mild differentiability conditions on the first derivative of the operator involved. The authors’ technique relies on the construction of a scalar sequence, not majorizing, that satisfies a system of recurrence relations, and guarantees the convergence of the method. The application is user-friendly and has certain advantages over Kantorovich’s majorant principle. First, it allows generalizations to be made of the results obtained under conditions of Newton-Kantorovich type and, second, it improves the results obtained through majorizing sequences. In addition, the authors extend the application of Newton’s method in Banach spaces from the modification of the domain of starting points. As a result, the scope of Kantorovich’s theory for Newton’s method is substantially broadened. Moreover, this technique can be applied to any iterative method.
This book is chiefly intended for researchers and (postgraduate) students working on nonlinear equations, as well as scientists in general with an interest in numerical analysis.
Authors and Affiliations
Bibliographic Information
Book Title: Mild Differentiability Conditions for Newton's Method in Banach Spaces
Authors: José Antonio Ezquerro Fernandez, Miguel Ángel Hernández Verón
Series Title: Frontiers in Mathematics
DOI: https://doi.org/10.1007/978-3-030-48702-7
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-48701-0Published: 04 July 2020
eBook ISBN: 978-3-030-48702-7Published: 03 July 2020
Series ISSN: 1660-8046
Series E-ISSN: 1660-8054
Edition Number: 1
Number of Pages: XIII, 178
Number of Illustrations: 6 b/w illustrations, 45 illustrations in colour
Topics: Operator Theory, Numerical Analysis, Integral Equations, Ordinary Differential Equations, Partial Differential Equations