Average-Case Analysis of Numerical Problems. 1st ed. 2000

種類:

電子ブック

責任表示:

by Klaus Ritter

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000

著者名:

• Ritter, Klaus.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1733

ISBN:

9783540455929 [3540455922]    

注記:

Linear problems: Definitions and a classical example -- Second-order results for linear problems -- Integration and approximation of univariate functions -- Linear problems for univariate functions with noisy data -- Integration and approximation of multivariate functions -- Nonlinear methods for linear problems -- Nonlinear problems.
The average-case analysis of numerical problems is the counterpart of the more traditional worst-case approach. The analysis of average error and cost leads to new insight on numerical problems as well as to new algorithms. The book provides a survey of results that were mainly obtained during the last 10 years and also contains new results. The problems under consideration include approximation/optimal recovery and numerical integration of univariate and multivariate functions as well as zero-finding and global optimization. Background material, e.g. on reproducing kernel Hilbert spaces and random fields, is provided.

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