Error estimates for the simplified iteratively regularized Gauss–Newton method in Banach spaces under a Morozov-type stopping rule

Abstract

Abstract Jin Qinian and Min Zhong [10] considered an iteratively regularized Gauss–Newton method in Banach spaces to find a stable approximate solution of the nonlinear ill-posed operator equation. They have considered a Morozov-type stopping rule (Rule 1) as one of the criterion to stop the iterations and studied the convergence analysis of the method. However, no error estimates have been obtained for this case. In this paper, we consider a modified variant of the method, namely, the simplified Gauss–Newton method under both an a priori as well as a Morozov-type stopping rule. In both cases, we obtain order optimal error estimates under Hölder-type approximate source conditions. An example of a parameter identification problem for which the method can be implemented is discussed in the paper.