Convergence and Applications of Newton-type Iterations
Ioannis K. Argyros
Convergence and Applications of Newton-type Iterations
Ioannis K. Argyros
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Omschrijving
Recent results in local convergence and semi-local convergence analysis constitute a natural framework for the theoretical study of iterative methods. Several classes of operators are considered, including operators without Lipschitz continuous derivatives, operators with high order derivatives, and analytic operators.
From the reviews:
"The book is devoted to iterative methods of approximative solving nonlinear operator equations … . The main part of the book deals with the classical Newton-Kantorovich method … . Undoubtedly, it can be used for an advanced study of the Newton-Kantorovich method and other iterative methods of approximate solving nonlinear operator equations. The reviewer recommends this book to all who deal with nonlinear operator equations and their approximate solutions." (Peter Zabreiko, Zentrablatt MATH, Vol. 1153, 2009)
“This monograph deals with Netwon-Kantorovich (N-K) type methods for solving equations in Banach spaces, presenting fundamental results as well as many of the author’s own developments. It is addressed to graduate students and researchers with background in linear algebra and numerical functional analysis. … it also as ‘a reference book for an advanced numerical-functional analysis course’, one would expect more details on applications in order to illustrate how such powerful numerical tools can be used.” (Elena Resmerita, Mathematical Reviews, Issue 2010 c)