Mild Differentiability Conditions for Newton's Method in Banach Spaces (Frontiers in Mathematics) - Softcover

Über die Autorin bzw. den Autor

Charlotte y Peter Fiell son dos autoridades en historia, teoría y crítica del diseño y han escrito más de sesenta libros sobre la materia, muchos de los cuales se han convertido en éxitos de ventas. También han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Diseño del siglo XX, El diseño industrial de la A a la Z, Scandinavian Design y Diseño del siglo XXI.

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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.