Mild Differentiability Conditions for Newton's Method in Banach Spaces
Language: English
Published by Birkhäuser, 2020
- Softcover
- New
Condition: New
US$ 63.49
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Mild Differentiability Conditions for Newton's Method in Banach Spaces | José Antonio Ezquerro Fernandez (u. a.) | Taschenbuch | Frontiers in Mathematics | xiii | Englisch | 2020 | Birkhäuser | EAN 9783030487010 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
Seller Inventory # 118263415
- Title
- Mild Differentiability Conditions for Newton's Method in Banach Spaces
- Author
- José Antonio Ezquerro Fernandez (u. a.)
- Publisher
- Birkhäuser
- Publication year
- 2020
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 3030487016
- ISBN 13
- 9783030487010
- Item weight
- 332 grams
- Dimensions
- 240 x 168 x 11 mm
- Series
- Book 43 of 48: Frontiers in Mathematics
- Seller catalogs
- Bücher
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.
"Synopsis" may belong to another edition of 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.
"About the title" may belong to another edition of this title.
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