Faculty Publications

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Author: search.filters.author.Padikkal, P.Subject: search.filters.subject.Hilbert scales

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    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.
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    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.
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    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.