Finite Dimensional Approximation of Simplified Gauss-Newton Scheme for Nonlinear Ill-Posed Problems

Abstract

We consider the finite dimensional approximation of simplified Gauss-Newton iterative scheme presented in [14] for solving nonlinear ill-posed problems. The convergence and convergent analysis of this scheme is carried out with both an a priori and an a posteriori parameter choice strategies. The error estimates are derived accordingly. We propose an order optimal parameter choice strategy for the regularization parameter, which gives the optimal convergence rate. Finally, we present numerical examples to verify the theoretical results.