A two step modified Newton method is considered for obtaining an approximate solution for the nonlinear ill-posed equationF(x)=fwhen the available data arefδwith‖f−fδ‖≤δand the operatorFis monotone. The derived error estimate under a general source condition onx0−x^is of optimal order; herex0is the initial guess andx^is the actual solution. The regularization parameter is chosen according to the adaptive method considered by Perverzev and Schock (2005). The computational results provided endorse the reliability and effectiveness of our method.
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