Abstract: This paper is devoted to the numerical solution of
large-scale linear ill-posed systems. A multilevel regularization
method is proposed. This method is based on a synthesis of
the Arnoldi-Tikhonov regularization technique and the multilevel
technique. We show that if the Arnoldi-Tikhonov method is
a regularization method, then the multilevel method is also a
regularization one. Numerical experiments presented in this paper
illustrate the effectiveness of the proposed method.
Abstract: In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable.