ON CONVERGENCE-RATES FOR THE ITERATIVELY REGULARIZED GAUSS-NEWTON METHOD

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