Iterated Tikhonov regularization with a general penalty term

Tikhonov regularization is one of the most popular approaches to solving linear discrete ill-posed problems. The choice of the regularization matrix may significantly affect the quality of the computed solution. When the regularization matrix is the identity, iterated Tikhonov regularization can yield computed approximate solutions of higher quality than (standard) Tikhonov regularization. This paper provides an analysis of iterated Tikhonov regularization with a regularization matrix different from the identity. Computed examples illustrate the performance of this method.