Mild Differentiability Conditions for Newton's Method in Banach Spaces
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Beschreibung
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.
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.
Presents a new iterative technique for solving nonlinear equations Substantially broadens the scope of Kantorovich’s theory for Newton’s method Intended for researchers and postgraduate students working on nonlinear equations
Autor*in
José Antonio Ezquerro Fernandez
Themen in »Mild Differentiability Conditions for Newton's Method in Banach Spaces«
Newton’s method semilocal convergence Kantorovich’s theory mild differentiability conditions recurrence relations Hammerstein integral equations conservative problems elliptic equations ordinary differential equations partial differential equations
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“This book is addressing researchers and advanced students interested in solving functional (like integral or differential) equations. The proofs are included in full detail and the results are extensively illustrated with practical applications.” (Adhemar Bultheel, zbMATH 1573.65003, 2026)
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