On convergence rates for the iteratively regularized Gauss-Newton method

In this paper we prove that the iteratively regularized Gauss-Newton method is a locally convergent method for solving nonlinear ill-posed problems, provided the nonlinear operator satisfies a certain smoothness condition. For perturbed data we propose a priori and a posteriori stopping rules that guarantee convergence of the iterates, if the noise level goes to zero. Under appropriate closeness and smoothness conditions on the exact solution we obtain the same convergence rates as for linear ill-posed problems.