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

Buch 43 von 48: Frontiers in Mathematics

Ezquerro Fernandez, José Antonio; Hernández Verón, Miguel Ángel

 
9783030487010: Mild Differentiability Conditions for Newton's Method in Banach Spaces (Frontiers in Mathematics)
Softcover
ISBN 10: 3030487016 ISBN 13: 9783030487010
Verlag: Birkhäuser, 2020

Inhaltsangabe

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.

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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.

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Verlag
Birkhäuser
Erscheinungsdatum
2020
Sprache
Englisch
ISBN 10 
3030487016
ISBN 13 
9783030487010
Einband
Taschenbuch
Auflage
1
Anzahl der Seiten
192
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