Probabilistic Analysis of Galerkin-Like Methods for the Fredholm Equation of the Second Kind

Abstract

This paper deals with the approximate solution of the Fredholm equation $u-T_Ku=f$ of the second kind from a probabilistic point of view. With Wiener type measures on the set of kernels and free terms we determine statistical features of the approximation process, i.e., the most likely rate of convergence and the dominating individual behavior. The analysis is carried out for a kind of Galerkin-like method.