Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations

Abstract

We investigate iterated Tikhonov methods coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. In the case of noisy data we propose a modi_cation, the so called loping iterated Tikhonov-Kaczmarz method, where a sequence of relaxation parameters is introduced and a di_erent stopping rule is used. Convergence analysis for this method is also provided.