Deterministic and Stochastic Error Bounds in Numerical Analysis (Lecture Notes in Mathematics) (Volume 1349)

Novak, Erich et al

ISBN 10: 3540503684 / ISBN 13: 9783540503682

Published by Springer, 1988

About this Item

Volume 1349. This is an ex-library book and may have the usual library/used-book markings inside.This book has soft covers. In fair condition, suitable as a study copy. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,350grams, ISBN:3540503684.

Seller Inventory # 7094531

Bibliographic Details

• Title: Deterministic and Stochastic Error Bounds in Numerical Analysis (Lecture Notes in Mathematics) (Volume 1349)
• Publisher: Springer
• Publication Date: 1988
• Language: English
• ISBN 10: 3540503684
• ISBN 13: 9783540503682
• Binding: Soft cover
• Condition: Fair
• Seller catalogs:
  • Mathematics

About this title

Synopsis

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).