Numerical approximation of a Tikhonov type regularizer by a discretized frozen steepest descent method

Abstract

We present a frozen regularized steepest descent method and its finite dimensional realization for obtaining an approximate solution for the nonlinear ill-posed operator equation F(x)=y. The proposed method is a modified form of the method considered by Argyros et al. (2014). The balancing principle considered by Pereverzev and Schock (2005) is used for choosing the regularization parameter. The error estimate is derived under a general source condition and is of optimal order. The provided numerical example proves the efficiency of the proposed method. 2017 Elsevier B.V.