Faculty Publications
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Item Fractional Tikhonov regularization method in Hilbert scales(Elsevier Inc. sinfo-f@elsevier.com, 2021) Mekoth, C.; George, S.; Padikkal, P.Fractional Tikhonov regularization method (FTRM) for linear ill-posed operator equations in the setting of Hilbert scales is being studied in this paper. Using a general Holder type source condition, we obtain an error estimate. A new parameter choice strategy is being proposed for choosing the regularization parameter in FTRM in the setting of Hilbert scales. Also, the proposed method is applied to the well known examples in the setting of Hilbert scales. © 2020 Elsevier Inc.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.