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Mild Differentiability Conditions for Newton's Method in Banach Spaces

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Mild Differentiability Conditions for Newton's Method in Banach Spaces/ by José Antonio Ezquerro Fernandez, Miguel Ángel Hernández Verón.
作者:	Ezquerro Fernandez, José Antonio.
其他作者:	Hernández Verón, Miguel Ángel.
面頁冊數:	XIII, 178 p. 51 illus., 45 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Partial Differential Equations. -
電子資源:	https://doi.org/10.1007/978-3-030-48702-7
ISBN:	9783030487027

Mild Differentiability Conditions for Newton's Method in Banach Spaces
Ezquerro Fernandez, José Antonio.

Mild Differentiability Conditions for Newton's Method in Banach Spaces[electronic resource] /by José Antonio Ezquerro Fernandez, Miguel Ángel Hernández Verón. - 1st ed. 2020. - XIII, 178 p. 51 illus., 45 illus. in color.online resource. - Frontiers in Mathematics,1660-8046. - Frontiers in Mathematics,.

Preface -- The Newton-Kantorovich theorem -- Operators with Lipschitz continuous first derivative -- Operators with Hölder continuous first derivative -- Operators with Hölder-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

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

671119
Partial Differential Equations.

LC Class. No.: QA329-329.9

Dewey Class. No.: 515.724

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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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