A modification of regularized newton-type method for nonlinear ill-posed problems

Abstract

A Modification of regularized Newton-type method for nonlinear ill-posed problems is considered. Using an a posteriori stopping rule proposed by Kaltenbacher, the convergence of the method is proved under certain conditions on the nonlinear operator. Optimal convergence rates are also shown under appropriate closeness and smoothness assumptions on the difference of the starting value and the solution. Some special cases of the method are also given. Numerical results confirm the corresponding theoretical statements. © 2010 Springer-Verlag.