Information Complexity of Multivariate Fredholm Integral Equations in Sobolev Classes

Abstract

In this paper, the complexity of full solution of Fredholm integral equations of the second kind with data from the Sobolev classWr2is studied. The exact order of information complexity is derived. The lower bound is proved using a Gelfand number technique. The upper bound is shown by providing a concrete algorithm of optimal order, based on a specific hyperbolic cross approximation of the kernel function. Numerical experiments are included, comparing the optimal algorithm with the standard Galerkin method.