One Newton-type method for the regularization of nonlinear ill-posed problems

In this paper we consider a combination of Newton's method with simplified Newton iteration for regularizing a nonlinear ill-posed operator equation. We show that under certain smoothness conditions on the nonlinear operator the method converge locally. For perturbed data we propose an a priori stopping rule which guarantees convergence of the iteration to a solution as the noise level goes to zero. Under appropriate closeness and smoothness assumptions on the starting value and the solution, we obtain convergence rates.