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Average-Case Analysis of Numerical Problems

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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.

Author(s): Klaus Ritter
Series: Lecture notes in mathematics 1733
Edition: 1
Publisher: Springer
Year: 2000

Language: English
Pages: 255
City: Berlin; New York

41ACNSTTH4L......Page 1
front-matter......Page 2
01Introduction......Page 10
02Definitions and a classical example......Page 19
03Second-order results for linear problems......Page 40
04Integration and approximation of univariate functions......Page 73
05Linear problems for univariate functions with noisy data......Page 128
06Integration and approximation of multivariate functions......Page 137
07Nonlinear methods for linear problems......Page 187
08Nonlinear problems......Page 216
back-matter......Page 229