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Deterministic and Stochastic Error Bounds in Numerical Analysis

  • Book
  • © 1988

Overview

Authors:
  1. Erich Novak
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1349)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-V
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  2. Introduction

    • Erich Novak
    Pages 1-8

  3. Deterministic error bounds

    • Erich Novak
    Pages 9-42

  4. Error bounds for monte carlo methods

    • Erich Novak
    Pages 43-65

  5. Average error bounds

    • Erich Novak
    Pages 66-89

  6. Back Matter

    Pages 90-113
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Keywords

About this book

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).

Bibliographic Information

  • Book Title: Deterministic and Stochastic Error Bounds in Numerical Analysis

  • Authors: Erich Novak

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0079792

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-50368-2Published: 26 October 1988

  • eBook ISBN: 978-3-540-45987-3Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 124

  • Topics: Numerical Analysis

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