Mild Differentiability Conditions for Newton's Method in Banach Spaces

Miguel Ángel Hernández Verón

ISBN 10: 3030487016 / ISBN 13: 9783030487010

Published by Springer International Publishing, 2020

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783030487010

Bibliographic Details

• Title: Mild Differentiability Conditions for Newton's Method in Banach Spaces
• Publisher: Springer International Publishing
• Publication Date: 2020
• Language: English
• ISBN 10: 3030487016
• ISBN 13: 9783030487010
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 240W x 168H x 11D millimeters 240 millimeters width by 168 millimeters height by 11 millimeters depth
• Weight: 332 grams

About this title

Synopsis

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.