The iterated regularization with perturbed operators and noisy data (Q1344600)

The method of iterated Tikhonov regularization with perturbed operators and noisy data for solving operator equations of the type \(Tx= y\) in Hilbert spaces is investigated. A crucial problem in Tikhonov's regularization is the choice of the regularization parameter in dependence on the noise. If \(T\) is exactly known Tikhonov's regularization done by \textit{J. T. King} and \textit{D. Chillingworth} [Numer. Funct. Anal. Optimization 1, 499-513 (1979; Zbl 0446.65026)] and Arcangeli's method proposed by \textit{H. W. Engl} and \textit{A. Neubauer} [Notes Rep. Math. Sci. Eng. 4, 97-125 (1987; Zbl 0627.65060)] lead to an optimal convergence rate. This paper is to provide an a posteriori parameter choice and a higher asymptotic convergence rate for the iterated Tikhonov regularization by using a generalized Arcangeli method. Convergence rates are estimated.