Convergence analysis of simplified Gauss–Newton iterative method under a heuristic rule

Jin and Wang (Inverse Probl. 34(3) (2018):035001) used a heuristic rule as a stopping criterion to terminate the iterations for the iteratively regularized Gauss–Newton method for getting stable approximate solution for nonlinear ill-posed operator equations. The advantage of using heuristic rule over the existing stopping rules is that, it does not require exact information about the noise level. In this paper, we do convergence analysis of the simplified generalized Gauss–Newton method under heuristic rule. We obtain rate of convergence results using the general form of source condition. We will also prove convergence of the method without using any source condition. We show the validity of the proposed algorithm using numerical examples.