Faculty Publications

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Subject: search.filters.subject.Ill-posed problem

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    Expanding the applicability of a Newton-Lavrentiev regularization method for ill-posed problems
    (Publishing House of the Romanian Academy Calea 13 Septembrie nr. 13, Sector 5, 050711. P.O. Box 5-42, Bucuresti, 2013) Argyros, I.K.; George, S.
    We present a semilocal convergence analysis for a simplified Newton-Lavrentiev regularization method for solving ill-posed problems in a Hilbert space setting. We use a center-Lipschitz instead of a Lipschitz condition in our conver-gence analysis. This way we obtain: weaker convergence criteria, tighter error bounds and more precise information on the location of the solution than in earlier studies (such as [13]).
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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 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)