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Finite dimensional realization of a quadratic convergence yielding iterative regularization method for ill-posed equations with monotone operators
(Elsevier Inc. usjcs@elsevier.com, 2016) Shubha, V.S.; George, S.; Padikkal, P.; Erappa, M.E.
Recently Jidesh et al. (2015), considered a quadratic convergence yielding iterative method for obtaining approximate solution to nonlinear ill-posed operator equation F(x)=y, where F: D(F) ? X ? X is a monotone operator and X is a real Hilbert space. In this paper we consider the finite dimensional realization of the method considered in Jidesh et al. (2015). Numerical example justifies our theoretical results. © 2015 Elsevier Inc. All rights reserved.
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.