## Information Complexity of Multivariate Fredholm Equations in Sobolev Classes

• In this paper, the complexity of full solution of Fredholm integral equations of the second kind with data from the Sobolev class $$W^r_2$$ is 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.