Lecture Notes in Mathematics

Deterministic and Stochastic Error Bounds in Numerical Analysis

Authors: Novak, Erich

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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).

Table of contents (4 chapters)

Buy this book

eBook $29.99
price for USA (gross)
  • ISBN 978-3-540-45987-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
price for USA
  • ISBN 978-3-540-50368-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Deterministic and Stochastic Error Bounds in Numerical Analysis
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1349
Copyright
1988
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-45987-3
DOI
10.1007/BFb0079792
Softcover ISBN
978-3-540-50368-2
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 124
Topics