Mild differentiability conditions for Newton's method in banach spaces
Ezquerro Fernandez, José Antonio
Mild differentiability conditions for Newton's method in banach spaces [Documento eletrónico] / José Antonio Ezquerro Fernandez, Miguel Ángel Hernández Verón. - Cham : Springer International Publishing : Birkhäuser , 2020 . - XIII, 178 p. : il.. - (Frontiers in Mathematics) 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.
Clicar aqui para aceder a um recurso externo
ISBN 978-3-030-48702-7
Operator theory
Numerical analysis
Integral equations
Differential equations
LCC QA329-329.9
Mild differentiability conditions for Newton's method in banach spaces [Documento eletrónico] / José Antonio Ezquerro Fernandez, Miguel Ángel Hernández Verón. - Cham : Springer International Publishing : Birkhäuser , 2020 . - XIII, 178 p. : il.. - (Frontiers in Mathematics) 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.
Clicar aqui para aceder a um recurso externo
ISBN 978-3-030-48702-7
Operator theory
Numerical analysis
Integral equations
Differential equations
LCC QA329-329.9
