Optimal Solution of Nonlinear Equations

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Krzysztof A. Sikorski (Department of Computer Science, Department of Computer Science, University of Utah, Salt Lake City)

Optimal Solution of Nonlinear Equations

Krzysztof A. Sikorski (Department of Computer Science, Department of Computer Science, University of Utah, Salt Lake City)

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Oxford University Press Inc
01 December 2000

Algebra; Calculus & mathematical analysis; Non-linear science; Maths for scientists; Maths for engineers

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.

By: Krzysztof A. Sikorski (Department of Computer Science Department of Computer Science University of Utah Salt Lake City)
Imprint: Oxford University Press Inc
Country of Publication: United States
Dimensions: Height: 243mm, Width: 160mm, Spine: 19mm
Weight: 548g
ISBN: 9780195106909
ISBN 10: 0195106903
Pages: 252
Publication Date: 01 December 2000
Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , A / AS level , Undergraduate
Format: Hardback
Publisher's Status: Active

1: Introduction 1.1: Basic Concepts 1.2: Formulation of the Problem 1.3: Annotations Bibliography 2: Nonlinear Equations 2.1: Univariate Problems 2.2: Multivariate Problems 2.3: Annotations Bibliography 3: Fixed Points - Contractive Functions 3.1: Univariate Problems 3.2: Multivariate Problems 3.3: Annotations Bibliography 4: Fixed Points - Noncontractive Functions 4.1: Univariate Problems 4.2: Multivariate Problems 4.3: Annotations Bibliography 5: Topological Degree Computation 5.1: Two Dimensional Lipschitz Functions 5.2: Lipschitz Functions in d Dimensions 5.3: Annotations Bibliography Index

Reviews for Optimal Solution of Nonlinear Equations

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 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