On broyden's method for the regularization of nonlinear ill-posed problems1

Abstract

This paper is concerned with nonlinear ill-posed operator equations F(x) = y and their approximate solution by a quasi-Newton method, namely a regularized version of Broyden's method. Under an assumption on the nonlinearity of F(which is shown to be fulfilled for several examples of inverse problems) and with an appropriate stopping rule, local convergence and convergence rates results are proven. The theoretical results are illustrated by numerical tests.