A fast multiscale Galerkin method for the first kind ill-posed integral equations via Tikhonov regularization

In this paper, we develop a fast multiscale Galerkin method to solve the Fredholm integral equations of the first kind via Tikhonov regularization. The method leads to fast solutions of discrete regularization methods. We obtain optimal convergence rates for approximate solutions with an a priori parameter choice and a kind of discrepancy principle. Finally, numerical experiments are given to illustrate the efficiency of the method.