Convergence of a Tikhonov Gradient Type-Method for Nonlinear Ill-Posed Equations

Abstract

In this study Tikhonov Gradient type-method is considered for nonlinear ill-posed operator equations. In our convergence analysis, we use hypotheses only on the first Frec?het derivative of F in contrast to the higher order Frec?het derivatives used in the earlier studies. We obtained optimal order error estimate by choosing the regularization parameter according to the adaptive method proposed by Pereverzev and Schock (SIAM J Numer Anal 43(5):2060 2076, 2005). 2017, Springer (India) Private Ltd.