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Mild differentiability conditions fo...

Ezquerro Fernandez, Jose Antonio.

Mild differentiability conditions for Newton's method in Banach spaces

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Mild differentiability conditions for Newton's method in Banach spacesby Jose Antonio Ezquerro Fernandez, Miguel Angel Hernandez Veron.
作者:	Ezquerro Fernandez, Jose Antonio.
其他作者:	Hernandez Veron, Miguel Angel.
出版者:	Cham :Springer International Publishing :2020.
面頁冊數:	xiii, 178 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Banach spaces.
電子資源:	https://doi.org/10.1007/978-3-030-48702-7
ISBN:	9783030487027$q(electronic bk.)

Mild differentiability conditions for Newton's method in Banach spaces
Ezquerro Fernandez, Jose Antonio.

Mild differentiability conditions for Newton's method in Banach spaces[electronic resource] /by Jose Antonio Ezquerro Fernandez, Miguel Angel Hernandez Veron. - Cham :Springer International Publishing :2020. - xiii, 178 p. :ill., digital ;24 cm. - Frontiers in mathematics,1660-8046. - Frontiers in mathematics..

Preface -- The Newton-Kantorovich theorem -- Operators with Lipschitz continuous first derivative -- Operators with Holder continuous first derivative -- Operators with Holder-type continuous first derivative -- Operators with w-Lipschitz continuous first derivative -- Improving the domain of starting points based on center conditions for the first derivative -- Operators with center w-Lipschitz continuous first derivative -- Using center w-Lipschitz conditions for the first derivative at auxiliary points.

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.

ISBN: 9783030487027$q(electronic bk.)

Standard No.: 10.1007/978-3-030-48702-7doiSubjects--Topical Terms:

199048
Banach spaces.

LC Class. No.: QA322.2 / .E978 2020

Dewey Class. No.: 515.732

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520 $a 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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