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Numerical approximation of a Tikhonov type regularizer by a discretized frozen steepest descent method
(Elsevier B.V., 2018) George, S.; Sabari, M.
We present a frozen regularized steepest descent method and its finite dimensional realization for obtaining an approximate solution for the nonlinear ill-posed operator equation F(x)=y. The proposed method is a modified form of the method considered by Argyros et al. (2014). The balancing principle considered by Pereverzev and Schock (2005) is used for choosing the regularization parameter. The error estimate is derived under a general source condition and is of optimal order. The provided numerical example proves the efficiency of the proposed method. © 2017 Elsevier B.V.
Modified Minimal Error Method for Nonlinear Ill-Posed Problems
(Walter de Gruyter GmbH cmam@cmam.info, 2018) Sabari, M.; George, S.
An error estimate for the minimal error method for nonlinear ill-posed problems under general a Hölder-type source condition is not known. We consider a modified minimal error method for nonlinear ill-posed problems. Using a Hölder-type source condition, we obtain an optimal order error estimate. We also consider the modified minimal error method with noisy data and provide an error estimate. © 2018 Walter de Gruyter GmbH, Berlin/Boston.