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
CONTENT
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
