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dc.contributor.authorGeorge, S.
dc.contributor.authorPareth, S.
dc.date.accessioned2020-03-31T06:51:36Z-
dc.date.available2020-03-31T06:51:36Z-
dc.date.issued2013
dc.identifier.citationJournal of Applied Analysis, 2013, Vol.19, 2, pp.181-196en_US
dc.identifier.uri10.1515/jaa-2013-0011
dc.identifier.urihttp://idr.nitk.ac.in/jspui/handle/123456789/9860-
dc.description.abstractMotivated 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.en_US
dc.titleAn application of Newton-type iterative method for the approximate implementation of Lavrentiev regularizationen_US
dc.typeArticleen_US
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