ON THE SEMILOCAL CONVERGENCE OF MODIFIED NEWTON-TIKHONOV REGULARIZATION METHOD FOR NONLINEAR ILL-POSED PROBLEMS

Abstract

In this study, we introduce a new modified Newton-Tikhonov method for ap-proximating a solution of nonlinear ill-posed problems. The proposed iteration convergesquadratically. Order optimal error bounds are given in case the regularization parameter ischosen a priori and by the adaptive method of Pereverzev and Schock(2005).