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An application of newton type iterative method for lavrentiev regularization for ill-posed equations: Finite dimensional realization
(2012) George, S.; Pareth, S.
In this paper, we consider, a finite dimensional realization of Newton type iterative method for Lavrentiev regularization of ill-posed equations. Precisely we consider the ill-posed equation F(x) = f when the available data is f ? with
Newton Lavrentiev regularization for ill-posed operator equations in Hilbert scales
(2013) George, S.; Pareth, S.; Kunhanandan, M.
In this paper we consider the two step method for approximately solving the ill-posed operator equation F(x)=f, where F:D(F) âŠ†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.