Optimal Solution of Nonlinear Equations

by Krzysztof A. Sikorski

Overview

Optimal Solution of Nonlinear Equations is a text/monograph designed to provide an overview of optimal computational methods for the solution of nonlinear equations, fixed points of contractive and noncontractive mapping, and for the computation of the topological degree. It is of interest to any reader working in the area of Information-Based Complexity. The worst-case settings are analyzed here. Several classes of functions are studied with special emphasis on tight complexity bounds and methods which are close to or achieve these bounds. Each chapter ends with exercises, including companies and open-ended research based exercises.

Product Details

ISBN-13:	9780195106909
Publisher:	Oxford University Press
Publication date:	01/18/2001
Edition description:	New Edition
Pages:	256
Product dimensions:	9.21(w) x 6.14(h) x 0.63(d)

About the Author

University of Utah, Salt Lake City

Table of Contents

1. Introduction1.1. Basic Concepts1.2. Formulation of the Problem1.3. AnnotationsBibliography2. Nonlinear Equations2.1. Univariate Problems2.2. Multivariate Problems2.3. AnnotationsBibliography3. Fixed Points - Contractive Functions3.1. Univariate Problems3.2. Multivariate Problems3.3. AnnotationsBibliography4. Fixed Points - Noncontractive Functions4.1. Univariate Problems4.2. Multivariate Problems4.3. AnnotationsBibliography5. Topological Degree Computation5.1. Two Dimensional Lipschitz Functions5.2. Lipschitz Functions in d Dimensions5.3. AnnotationsBibliographyIndex

Editorial Reviews

"The volume under consideration studies the complexity of the following nonlinear problems in the worst-case setting: approximating the solution of nonlinear equations, approximating fixed points, and calculating topological degree. . . . At the end of each chapter, there are historical annotations and a bibliography. The author is a leading researcher in these areas, and well qualified to write such a monograph. The book is complete, with proofs given in full detail. . . . [T]his monograph will be a useful tool, both for those who wish to learn about complexity and optimal algorithms for nonlinear equations, as well as for those who are already working in this area." — Mathematical Reviews

From the Publisher

Sikorski (a mathematician whose academic affiliations are not noted) provides an overview of optimal computations methods for the solution of nonlinear equations, fixed points of contractive and noncontractive mappings, and for the computation of the topological degree. Several classes of functions are examined, with emphasis placed on tight complexity bounds and methods that are close to or achieve these bounds. Pseudocodes and numerical tests of several methods are shown. A set of exercises follows each section of the text. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews