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Expanding the applicability of an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems
(Springer-Verlag Italia s.r.l., 2019) Argyros, I.K.; Cho, Y.J.; George, S.; Xiao, Y.
We expand the applicability of an a posteriori parameter choice strategy for Tikhonov regularization of the nonlinear ill-posed problem presented in Jin and Hou (Numer Math 83:139–159, 1999) by weakening the conditions needed in Jin and Hou [13]. Using a center-type Lipschitz condition instead of a Lipschitz-type condition used in Jin and Hou [13], Scherzer et al. (SIAM J Numer Anal 30:1796–1838, 1993), we obtain a tighter convergence analysis. Numerical examples are presented to show that our results apply but earlier ones do not apply to solve equations. © 2019, The Royal Academy of Sciences, Madrid.
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.