Matches in Harvard for { <http://id.lib.harvard.edu/aleph/001597005/catalog> ?p ?o. }
Showing items 1 to 31 of
31
with 100 items per page.
- catalog abstract "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).".
- catalog contributor b2278650.
- catalog created "c1988.".
- catalog date "1988".
- catalog date "c1988.".
- catalog dateCopyrighted "c1988.".
- catalog description "Bibliography: p. [100]-109.".
- catalog description "Contents: Introduction -- Deterministic Error Bounds -- Error Bounds for Monte Carlo Methods -- Average Error Bounds -- Appendix: Existence and Uniqueness of Optimal Algorithms -- Bibliography -- Notations -- Index.".
- catalog description "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).".
- catalog extent "113 p. ;".
- catalog hasFormat "Deterministic and stochastic error bounds in numerical analysis.".
- catalog identifier "0387503684 (U.S.)".
- catalog identifier "3540503684".
- catalog isFormatOf "Deterministic and stochastic error bounds in numerical analysis.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1349.".
- catalog isPartOf "Lecture notes in mathematics ; 1349".
- catalog issued "1988".
- catalog issued "c1988.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog relation "Deterministic and stochastic error bounds in numerical analysis.".
- catalog subject "510 s 519.4 19".
- catalog subject "Approximation theory.".
- catalog subject "Error analysis (Mathematics)".
- catalog subject "Mathematics.".
- catalog subject "Monte Carlo method.".
- catalog subject "Numerical analysis.".
- catalog subject "QA3 .L28 no. 1349 QA297".
- catalog tableOfContents "Contents: Introduction -- Deterministic Error Bounds -- Error Bounds for Monte Carlo Methods -- Average Error Bounds -- Appendix: Existence and Uniqueness of Optimal Algorithms -- Bibliography -- Notations -- Index.".
- catalog title "Deterministic and stochastic error bounds in numerical analysis / Erich Novak.".
- catalog type "text".