Mild Differentiability Conditions for Newton's Method in Banach Spaces (Frontiers in Mathematics) - Softcover

Ezquerro Fernandez, José Antonio; Hernández Verón, Miguel Ángel

Softcover

ISBN 10: 3030487016 ISBN 13: 9783030487010

Publisher: Birkhäuser, 2020

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.

About this title

From the Back Cover

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 ischiefly intended for researchers and (postgraduate) students working on nonlinear equations, as well as scientists in general with an interest in numerical analysis.

Edition details

• Publisher: Birkhäuser
• Publication date: 2020
• Language: English
• ISBN 10: 3030487016
• ISBN 13: 9783030487010
• Binding: Paperback
• Edition number: 1
• Number of pages: 191