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Mild Differentiability Conditions for Newton's Method in Banach Spaces (Paperback, 1st ed. 2020)
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Mild Differentiability Conditions for Newton's Method in Banach Spaces (Paperback, 1st ed. 2020)
Series: Frontiers in Mathematics
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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 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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