TY - JOUR
T1 - Finite dimensional realization of fractional Tikhonov regularization method in Hilbert scales
AU - Mekoth, Chitra
AU - George, Santhosh
AU - Jidesh, P.
AU - Erappa, Shobha M.
N1 - Publisher Copyright:
© 2021 The Author(s)
PY - 2022/6
Y1 - 2022/6
N2 - 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.
AB - 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.
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U2 - 10.1016/j.padiff.2021.100246
DO - 10.1016/j.padiff.2021.100246
M3 - Article
AN - SCOPUS:85125837556
SN - 2666-8181
VL - 5
JO - Partial Differential Equations in Applied Mathematics
JF - Partial Differential Equations in Applied Mathematics
M1 - 100246
ER -