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Title: Iterative regularization methods for ill-posed operator equations in Hilbert scales
Authors: Argyros, I.K.
George, S.
Jidesh, P.
Issue Date: 2017
Citation: Nonlinear Studies, 2017, Vol.24, 2, pp.257-271
Abstract: In this paper we report on a method for regularizing a nonlinear ill-posed operator equation in Hilbert scales. The proposed method is a combination of Lavrentiev regularization method and a Modified Newton's method in Hilbert scales . Under the assumptions that the operator F is continu- ously differentiable with a Lipschitz-continuous first derivative and that the solution of (1.1) fulfils a general source condition, we give an optimal order convergence rate result with respect to the general source function. CSP - Cambridge, UK; I & S - Florida, USA, 2017.
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