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Deterministic and Stochastic Error Bounds in Numerical Analysis

  • Authors
  • Erich┬áNovak

Part of the Lecture Notes in Mathematics book series (LNM, volume 1349)

Table of contents

  1. Front Matter
    Pages I-V
  2. Erich Novak
    Pages 1-8
  3. Erich Novak
    Pages 9-42
  4. Erich Novak
    Pages 43-65
  5. Erich Novak
    Pages 66-89
  6. Back Matter
    Pages 90-113

About this book

Introduction

In these notes different deterministic and stochastic error bounds of numerical analysis are investigated. For many computational problems we have only partial information (such as n function values) and consequently they can only be solved with uncertainty in the answer. Optimal methods and optimal error bounds are sought if only the type of information is indicated. First, worst case error bounds and their relation to the theory of n-widths are considered; special problems such approximation, optimization, and integration for different function classes are studied and adaptive and nonadaptive methods are compared. Deterministic (worst case) error bounds are often unrealistic and should be complemented by different average error bounds. The error of Monte Carlo methods and the average error of deterministic methods are discussed as are the conceptual difficulties of different average errors. An appendix deals with the existence and uniqueness of optimal methods. This book is an introduction to the area and also a research monograph containing new results. It is addressd to a general mathematical audience as well as specialists in the areas of numerical analysis and approximation theory (especially optimal recovery and information-based complexity).

Keywords

Approximation Monte Carlo method algorithms approximation theory calculus numerical analysis optimization

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0079792
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-50368-2
  • Online ISBN 978-3-540-45987-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site