Optimal Solution of Nonlinear Equations.
Title:
Optimal Solution of Nonlinear Equations.
Author:
Sikorski, Krzysztof A.
ISBN:
9780198026679
Personal Author:
Physical Description:
1 online resource (253 pages)
Contents:
Contents -- 1 Introduction -- 1.1 Basic Concepts -- 1.2 Formulation of the Problem -- 1.2.1 Computational Methods -- 1.2.2 Optimal Complexity Methods -- 1.2.3 Asymptotic Setting -- 1.2.4 Exercises -- 1.3 Annotations -- Bibliography -- 2 Nonlinear Equations -- 2.1 Univariate Problems -- 2.1.1 Optimality of the Bisection Method -- 2.1.2 Root Criterion in C[sup(∞)] -- 2.1.3 Residual Criterion in W[sup(r)][sub(∞)] -- 2.1.4 General Error Criterion in C[sup(∞)] and W[sup(∞)][sub(r)] -- 2.1.5 Polynomial Equations -- 2.1.6 Asymptotic Optimality of the Bisection Method -- 2.1.7 Exercises -- 2.2 Multivariate Problems -- 2.2.1 Function with Nonzero Topological Degree -- 2.2.2 Lipschitz Functions -- 2.2.3 Exercises -- 2.3 Annotations -- 2.3.1 Overview and brief history -- 2.3.2 Specific Comments -- Bibliography -- 3 Fixed Points-Contractive Functions -- 3.1 Univariate Problems -- 3.1.1 Relative Error Criterion -- 3.1.2 Absolute Error Criterion -- 3.1.3 Exercises -- 3.2 Multivariate Problems -- 3.2.1 A Constructive Lemma -- 3.2.2 Ball Iteration -- 3.2.3 Ellipsoid Iteration -- 3.2.4 Centroid Method -- 3.2.5 Numerical Tests -- 3.2.6 Exercises -- 3.3 Annotations -- 3.3.1 Specific Comments -- Bibliography -- 4 Fixed Points-Noncontractive Functions -- 4.1 Univariate Problems -- 4.1.1 Minimal Cardinality Number -- 4.1.2 The FPE-A Method -- 4.1.3 Exercises -- 4.2 Multivariate Problems -- 4.2.1 Absolute Error Criterion -- 4.2.2 Exercises -- 4.3 Annotations -- 4.3.1 General Comments -- 4.3.2 Residual Error Criterion -- 4.3.3 Specific Comments -- Bibliography -- 5 Topological Degree Computation -- 5.1 Two-Dimensional Lipschitz Functions -- 5.1.1 Basic Definitions -- 5.1.2 Lower Bound on the Minimal Cardinality Number -- 5.1.3 Minimal Cardinality Number -- 5.1.4 Complexity of the Problem -- 5.1.5 Numerical Experiments -- 5.1.6 Exercises.
5.2 Lipschitz Function in d Dimensions -- 5.2.1 Basic Definitions -- 5.2.2 Information N[sup(*)] -- 5.2.3 Algorithm Ø[sup(*)] Using Information N[sup(*)] -- 5.2.4 Lower Bound on the Minimal -- 5.2.5 Exercises -- 5.3 Annotations -- 5.3.1 Specific Comments -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V -- W -- X -- Y -- Z.
Abstract:
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.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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