Numerical solution of integral equations,fast algorithms and Krein-Sobolev equation

Summary This paper contains a unified rigorous approach for the treatment of fast numerical algorithms for different classes of Fredholm integral equations of second kind. The Krein-Sobolev functional-differential nonlinear equation for the resolvent provides the ground for a unified approach. New results concerning the general analysis of the Krein-Sobolev equation and the convergence and stability of related numerical schemes are also presented.