On a class of frozen regularized Gauss-Newton methods for nonlinear inverse problems

Abstract

In this paper we consider a class of regularized Gauss-Newton methods for solving nonlinear inverse problems for which an a posteriori stopping rule is proposed to terminate the iteration. Such methods have the frozen feature that they require only the computation of the Fr´echet derivative at the initial approximation. Thus the computational work is considerably reduced. Under certain mild conditions, we give the convergence analysis and derive various estimates, including the order optimality, on these methods.