Two-parameter discrepancy principle for combined projection and Tikhonov regularization of ill-posed problems

Abstract

Abstract. For solving a linear ill-posed problem, a combination of Tikhonov regularization and a finite dimensional projection method is considered. In the present paper we treat the dimension of the projection as the second parameter of regularization. The method using the discrepancy set of all regularization parameter pairs which satisfy a certain discrepancy principle is investigated. For the case of truncated SVD and LSQ projection methods, under the standard source conditions, an order of convergence is derived. This order of convergence is optimal under the same conditions as those for Tikhonov regularization with the discrepancy principle and without additional discretization.