Information complexity of projection algorithms for the solution of Fredholm equations of the first kind. I

Abstract

We construct a new system of discretization of the Fredholm integral equations of the first kind with linear compact operators A and free terms from the set Range (A(A*A)^V), v > 1/2. The approach proposed enables one to obtain the optimal order of error on such classes of equations by using a considerably smaller amount of discrete information as compared with standard schemes.