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 Frechet derivative of F in contrast to the higher order Frechet 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).
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