Please use this identifier to cite or link to this item: http://idr.nitk.ac.in/jspui/handle/123456789/9860
Title: An application of Newton-type iterative method for the approximate implementation of Lavrentiev regularization
Authors: George, S.
Pareth, S.
Issue Date: 2013
Citation: Journal of Applied Analysis, 2013, Vol.19, 2, pp.181-196
Abstract: Motivated by the two-step directional Newton method considered by Argyros and Hilout (2010) for approximating a zero x* of a differentiable function F defined on a convex set D of a Hilbert space H, we consider a two-step Newton-Lavrentiev method (TSNLM) for obtaining an approximate solution to the nonlinear ill-posed operator equation F(x) = f , where F : D(F) ? X ? X is a nonlinear monotone operator defined on a real Hilbert space X. It is assumed that F(x) = f and that the only available data are f? with f - f? = ? ?. We prove that the TSNLM converges cubically to a solution of the equation F(x)+?(x-xo) = f? (such solution is an approximation of O x) where x0 is the initial guess. Under a general source condition on x0- x?, we derive order optimal error bounds by choosing the regularization parameter ? according to the balancing principle considered by Perverzev and Schock (2005). The computational results provided endorse the reliability and effectiveness of our method. 2013 by Walter de Gruyter Berlin Boston.
URI: 10.1515/jaa-2013-0011
http://idr.nitk.ac.in/jspui/handle/123456789/9860
Appears in Collections:1. Journal Articles

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