Faculty Publications
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Publications by NITK Faculty
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Item A two step newton type iteration for ill-posed Hammerstein type operator equations in Hilbert scales(Rocky Mountain Mathematics Consortium PO Box 871904 Tempe AZ 85287-1804, 2014) Erappa, M.E.; George, S.; Kunhanandan, M.In this paper regularized solutions of ill-posed Hammerstein type operator equation KF(x) = y, where K : X ? Y is a bounded linear operator with non-closed range and F : X ? X is non-linear, are obtained by a two step Newton type iterative method in Hilbert scales, where the available data is y? in place of actual data y withItem Iterative regularization methods for ill-posed operator equations in Hilbert scales(Cambridge Scientific Publishers jonathan.mckenna@touchbriefings.com, 2017) Argyros, I.K.; George, S.; Padikkal, P.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.Item Projection method for Fractional Lavrentiev Regularisation method in Hilbert scales(Springer Science and Business Media B.V., 2022) Mekoth, C.; George, S.; Padikkal, P.; Cho, Y.J.We study finite dimensional Fractional Lavrentiev Regularization (FLR) method for linear ill-posed operator equations in the Hilbert scales. We obtain an optimal order error estimate under Hölder type source condition and under a parameter choice strategy. Numerical experiments confirming the theoretical results are also given. © 2022, The Author(s), under exclusive licence to The Forum D’Analystes.Item Finite dimensional realization of fractional Tikhonov regularization method in Hilbert scales(Elsevier B.V., 2022) Mekoth, C.; George, S.; Padikkal, J.; Erappa, S.M.One of the intuitive restrictions of infinite dimensional Fractional Tikhonov Regularization Method (FTRM) for ill-posed operator equations is its numerical realization. This paper addresses the issue to a considerable extent by using its finite dimensional realization in the setting of Hilbert scales. Using adaptive parameter choice strategy, we choose the regularization parameter and obtain an optimal order error estimate. Also, the proposed method is applied to the well known examples in the setting of Hilbert scales. © 2021 The Author(s)Item Finite dimensional realization of a parameter choice strategy for fractional Tikhonov regularization method in Hilbert scales(Hacettepe University, 2023) Mekoth, C.; George, S.; Padikkal, P.One of the most crucial parts of applying a regularization method to solve an ill-posed problem is choosing a regularization parameter to obtain an optimal order error estimate. In this paper, we consider the finite dimensional realization of the parameter choice strategy proposed in [C. Mekoth, S. George and P. Jidesh, Appl. Math. Comput. 392, 125701, 2021] for Fractional Tikhonov regularization method for linear ill-posed operator equations in the setting of Hilbert scales. © 2023, Hacettepe University. All rights reserved.