Convergence and Applications of Newton-type Iterations

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ISBN: 1441924922
ISBN 13: 9781441924926
Autor: Argyros, Ioannis K
Verlag: Springer Verlag GmbH
Umfang: xvi, 56 S.
Erscheinungsdatum: 29.10.2010
Auflage: 1/2008
Produktform: Kartoniert
Einband: KT

Recent results in local convergence and semi-local convergence analysis constitute a natural framework for the theoretical study of iterative methods. This monograph provides a comprehensive study of both basic theory and new results in the area. Each chapter contains new theoretical results and important applications in engineering, modeling dynamic economic systems, input-output systems, optimization problems, and nonlinear and linear differential equations. Several classes of operators are considered, including operators without Lipschitz continuous derivatives, operators with high order derivatives, and analytic operators. Each section is self-contained. Examples are used to illustrate the theory and exercises are included at the end of each chapter. The book assumes a basic background in linear algebra and numerical functional analysis. Graduate students and researchers will find this book useful. It may be used as a self-study reference or as a supplementary text for an advanced course in numerical functional analysis.

Artikelnummer: 962008 Kategorie:

Beschreibung

InhaltsangabeOperators 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.

Inhaltsverzeichnis

Preface.- Table of Contents.- 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.- Point-to-Set Mappings.- The Newton-Kantorovich Theorem and Mathematical Programming.- Glossary of Symbols.- Bibliography.

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