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Title: Finite dimensional realization of a Tikhonov gradient type-method under weak conditions
Authors: Shubha, V.S.
George, S.
Jidesh, P.
Issue Date: 2016
Citation: Rendiconti del Circolo Matematico di Palermo, 2016, Vol.65, 3, pp.395-410
Abstract: In this paper we consider projection techniques to obtain the finite dimensional realization of a Tikhonov gradient type-method considered in George et al. (Local convergence of a Tikhonov gradient type-method under weak conditions, communicated, 2016) for approximating a solution x^ of the nonlinear ill-posed operator equation F(x) = y. The main advantage of the proposed method is that the inverse of the operator F is not involved in the method. The regularization parameter is chosen according to the adaptive method considered by Pereverzev and Schock (SIAM J Numer Anal 43(5):2060 2076, 2005). We also derive optimal stopping conditions on the number of iterations necessary for obtaining the optimal order of convergence. Using two numerical examples we compare our results with an existing method to justify the theoretical results. 2016, Springer-Verlag Italia.
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