A numerical method for solving nonlinear ill-posed problems

A two-step iterative process for the numerical solution of nonlinear problems is suggested. In order to avoid the ill-posed inversion of the Frechet derivative operator, some regularization parameter is introduced. A convergence theorem is proved. The proposed method is illustrated by a numerical example in which a nonlinear inverse problem of gravimetry is considered. Based on the results of the numerical experiments practical recommendations for the choice of the regularization parameter are given. Some other iterative schemes are considered.