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Title: | Newton Lavrentiev regularization for ill-posed operator equations in Hilbert scales |
Authors: | George, S. Pareth, S. Kunhanandan, M. |
Issue Date: | 2013 |
Citation: | Applied Mathematics and Computation, 2013, Vol.219, 24, pp.11191-11197 |
Abstract: | In this paper we consider the two step method for approximately solving the 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, in the setting of Hilbert scales. We derive the error estimates by selecting the regularization parameter ? according to the adaptive method considered by Pereverzev and Schock in (2005), when the available data is f? with ?-f-f??- ??. The error estimate obtained in the setting of Hilbert scales { Xr}r?R generated by a densely defined, linear, unbounded, strictly positive self adjoint operator L:D(L)X?X is of optimal order. 2013 Elsevier Inc. All rights reserved. |
URI: | http://idr.nitk.ac.in/jspui/handle/123456789/12231 |
Appears in Collections: | 1. Journal Articles |
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