Please use this identifier to cite or link to this item: http://idr.nitk.ac.in/jspui/handle/123456789/9851
Title: An analysis of Lavrentiev regularization method and Newton type process for nonlinear ill-posed problems
Authors: Vasin, V.
George, S.
Issue Date: 2014
Citation: Applied Mathematics and Computation, 2014, Vol.230, , pp.406-413
Abstract: In this paper we consider the Lavrentiev regularization method and a modified Newton method for obtaining stable approximate solution to nonlinear ill-posed operator equations F(x)=y where F:D(F)?X?X is a nonlinear monotone operator or F?(x0) is nonnegative selfadjoint operator defined on a real Hilbert space X. We assume that only a noisy data y??X with ?y- y???? are available. Further we assume that Fr chet derivative F? of F satisfies center-type Lipschitz condition. A priori choice of regularization parameter is presented. We proved that under a general source condition on x0-x?, the error ?x?-xn,??? between the regularized approximation xn,??(x0,??;=x0) and the solution x? is of optimal order. In the concluding section the algorithm is applied to numerical solution of the inverse gravimetry problem. 2013 Elsevier Inc. All rights reserved.
URI: 10.1016/j.amc.2013.12.104
http://idr.nitk.ac.in/jspui/handle/123456789/9851
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