Modified iterated Tikhonov methods for solving systems of nonlinearill-posed equations

Abstract

We investigate iterated Tikhonov methods coupled with a Kaczmarz strategyfor obtaining stable solutions of nonlinear systems of ill-posed operatorequations. We show that the proposed method is a convergent regularizationmethod.In the case of noisy data we propose a modification, the so calledloping iterated Tikhonov-Kaczmarz method, where a sequence of relaxationparameters is introduced and a different stopping rule is used. Convergenceanalysis for this method is also provided.