Optimal Solution of Nonlinear Equations
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Optimal Solution of Nonlinear Equations

Optimal Solution of Nonlinear Equations


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About the Book

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 analysed here. Several classes of functions are studied with special empahsis 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.

Table of Contents:
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

Review :
"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


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Product Details
  • ISBN-13: 9780195106909
  • Publisher: Oxford University Press Inc
  • Publisher Imprint: Oxford University Press Inc
  • Height: 156 mm
  • No of Pages: 256
  • Spine Width: 16 mm
  • Width: 234 mm
  • ISBN-10: 0195106903
  • Publisher Date: 15 Feb 2001
  • Binding: Hardback
  • Language: English
  • Returnable: N
  • Weight: 535 gr


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