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

In this paper we develop a fast multiscale Galerkin method to solve the ill-posed integral equation via iterated Tikhonov regularization. This method leads to fast solutions of discrete iterated Tikhonov regularization. The convergence rates of iterated Tikhonov regularization are achieved by using a modified discrepancy principle. Finally, numerical experiments are given to illustrate the efficiency of the method.