A fast multiscale Galerkin method for ill-posed integral equations with not exactly given input data via Tikhonov regularization

Abstract. In this paper we develop a fast multiscale Galerkin method solving ill-posed integral equations with not exactly given input data via Tikhonov regularization. The method leads to fast solutions of discrete Tikhonov regularization. The convergence rates of the Tikhonov regularization are achieved by using a modified discrepancy principle. Finally, numerical experiments are given to illustrate the efficiency of the method.