CONTINUOUS ANALOG OF THE GAUSS–NEWTON METHOD

Abstract

A Continuous Analog of discrete Gauss–Newton Method (CAGNM) for numerical solution of nonlinear problems is suggested. In order to avoid the ill-posed inversion of the Fréchet derivative operator, some regularization function is introduced. For the CAGNM, 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 function are given.