Ioannis K. Argyros

Convergence and Applications of Newton-type Iterations (eBook, PDF)

• Format: PDF

Produktbeschreibung

This monograph is devoted to a comprehensive treatment of iterative methods for solving nonlinear equations with particular emphasis on semilocal convergence analysis. Theoretical results are applied to engineering, dynamic economic systems, input-output systems, nonlinear and linear differential equations, and optimization problems. Accompanied by many exercises, some with solutions, the book may be used as a supplementary text in the classroom for seminars in advanced numerical and functional analysis or computer science.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 56
• Erscheinungstermin: 12. Juni 2008
• Englisch
• ISBN-13: 9780387727431
• Artikelnr.: 37286553

Inhaltsangabe

Operators and Equations.- The Newton Kantorovich (NK) Method.- Applications of the Weaker Version of the NK Theorem.- Special Methods.- Newton-like Methods.- Analytic Computational Complexity We Are Concerned with the Choice of Initial Approximations.- Variational Inequalities.- Convergence Involving Operators with Outer or Generalized Inverses.- Convergence on Generalized Banach Spaces: Improving Error Bounds and Weakening of Convergence Conditions.- Point to Set Mappings.- The Newton Kantorovich Theorem and Mathematical Programming.

Rezensionen

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)