Newton type iteration for Tikhonov regularization of non-linear ill-posed Hammerstein type equations

Abstract

An iterative method is investigated for a nonlinear ill-posed Hammerstein type operator equation KF(x)=f. We use a center-type Lipschitz condition in our convergence analysis instead of the usual Lipschitz condition. The adaptive method of Pereverzev and Schock (SIAM J. Numer. Anal. 43(5):2060-2076, 2005) is used for choosing the regularization parameter. The optimality of this method is proved under a general source condition involving the Fr chet derivative of F at some initial guess x 0. A numerical example of nonlinear integral equation shows the efficiency of this procedure. 2013 Korean Society for Computational and Applied Mathematics.