On the asymptotic order of accuracy of Tikhonov regularization

In this paper, the rate of convergence and the order of accuracy (with respect to the error level in the data) of Tikhonov's method for approximating the minimal-norm least-square solution of an ill-posed operator equation is investigated. It is shown that, in general, this rate of convergence is arbitrarily small. It is further shown how this rate depends on some smoothness properties of the solution. All results describe optimal orders.