Morozov's discrepancy principle for Tikhonov regularization of severely ill-posed problems in finite-dimensional subspaces.

In this paper severely ill-posed problems are studied which are represented in the form of linear operator equations with infinitely smoothing operators but with solutions having only a finite smoothness. It is well known, that the combination of Morozov's discrepancy principle and a finite dimensional version of the ordinary Tikhonov regularization is not always optimal because of its saturation property. Here it is shown, that this combination is always order-optimal in the case of severely ill-posed problems.