Average-Case Analysis of Numerical 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.