Overview

In this text the author develops the theory of the complexity of the solution to differential and integral equations and discusses the relationship between the worst-case setting and two related problems: the average-case setting and the probalistic setting.

Full Product Details

Author:   A.G. Werschulz
Publisher:   Oxford University Press
Imprint:   Oxford University Press
Dimensions:   Width: 16.40cm , Height: 2.50cm , Length: 24.10cm
Weight:   0.702kg
ISBN:  

9780198535898

ISBN 10:   0198535899
Pages:   342
Publication Date:   29 August 1991
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
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Table of Contents

Introduction; EXAMPLE: A TWO-POINT BOUNDARY VALUE PROBLEM: Introduction; Error, cost, and complexity; A minimal error algorithm; Complexity bounds; Comparison with the finite element method; Standard information; Final remarks; GENERAL FORMULATION: Introduction; Problem formulation; Information; Model of computation; Algorithms, their errors, and their costs; Complexity; Randomized setting; Asymptotic setting; THE WORST CASE SETTING: GENERAL RESULTS: Introduction; Radius and diameter; Complexity; Linear problems; The residual error criterion; ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS IN THE WORST CASE SETTING; Introduction; Variational elliptic boundary value problems; Problem formulation; The normed case with arbitrary linear information; The normed case with standard information; The seminormed case; Can adaption ever help?; OTHER PROBLEMS IN THE WORST CASE SETTING: Introduction; Linear elliptic systems; Fredholm problems of the second kind; Ill-posed problems; Ordinary differential equations; THE AVERAGE CASE SETTING: Introduction; Some basic measure theory; General results for the average case setting; Complexity of shift-invariant problems; Ill-posed problems; The probabilistic setting; COMPLEXITY IN THE ASYMPTOTIC AND RANDOMIZED SETTINGS: Introduction; Asymptotic setting; Randomized setting; Appendices; Bibliography.

Reviews

'This book ... is a most welcome addition to the theoretical computer science and numerical analysis literature. Though it is intended as a summary of current research, it is of the quality that would make it an excellent textbook on the subject for advanced numerical analysis and computer science courses .. it reads easily and lucidly.' R.S. Andersen 'An excellent and accessible introduction to the complexity of basic arithmetic operations ... it adds an interesting new dimension to the study of numerical methods for the solution of PDEs.' Notices of the A.M.S.

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