Probabilistic analysis of numerical methods for integral equations
Numerical problems and algorithms for solving Fredholm integral equations are analyzed from a probabilistic point of view. The probability measures on the set of right-hand sides and on the set of kernels are fixed. The author uses Wiener type measures which are naturally related to the scale of Sobolev spaces. This allows to extend the comparison between worst and probabilistic cases. Statistical features of the approximation process - the most likely rate of convergence and the dominating individual behaviour are determined. Two typical numerical methods are studied - the Galerkin and the iterated Galerkin method.
scientific article; zbMATH DE number 4211457
scientific article