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Title: | Expanding the applicability of Tikhonov's regularization and iterative approximation for ill-posed problems |
Authors: | Vasin, V. George, S. |
Issue Date: | 2014 |
Citation: | Journal of Inverse and Ill-Posed Problems, 2014, Vol.22, 4, pp.593-607 |
Abstract: | Recently, Vasin [J. Inverse Ill-Posed Probl. 21 (2013), 109-123] considered a new iterative method for approximately solving nonlinear ill-posed operator equation in Hilbert spaces. In this paper we introduce a modified form of the method considered by Vasin. This paper weakens the conditions needed in the existing results. We use a center-type Lipschitz condition in our convergence analysis instead of a Lipschitz-type condition used in [J. Inverse Ill-Posed Probl. 21 (2013), 109-123]. This way a tighter convergence analysis is obtained and under less computational cost, since the more precise and easier to compute center-Lipschitz instead of the Lipschitz constant is used in the convergence analysis. Order optimal error bounds are given in case the regularization parameter is chosen a priori and by the adaptive method of Pereverzev and Schock [SIAM J. Numer. Anal. 43 (2005), 2060-2076]. A numerical example of a nonlinear integral equation proves the efficiency of the proposed method. 2014 by De Gruyter. |
URI: | http://idr.nitk.ac.in/jspui/handle/123456789/11121 |
Appears in Collections: | 1. Journal Articles |
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