Two-Step Modified Newton Method for Nonlinear Lavrentiev Regularization

A two step modified Newton method is considered for obtaining an approximate solution for the nonlinear ill-posed equation ()= when the available data are with ‖−‖≤ and the operator is monotone. The derived error estimate under a general source condition on 0− is of optimal order; here 0 is the initial guess and is the actual solution. The regularization parameter is chosen according to the adaptive method considered by Perverzev and Schock (2005). The computational results provided endorse the reliability and effectiveness of our method.