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Author: search.filters.author.Sabari, M.Subject: search.filters.subject.Ill-posed operator equation

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    Convergence rate results for steepest descent type method for nonlinear ill-posed equations
    (Elsevier Inc. usjcs@elsevier.com, 2017) George, S.; Sabari, M.
    Convergence rate result for a modified steepest descent method and a modified minimal error method for the solution of nonlinear ill-posed operator equation have been proved with noisy data. To our knowledge, convergence rate result for the steepest descent method and minimal error method with noisy data are not known. We provide a convergence rate results for these methods with noisy data. The result in this paper are obtained under less computational cost when compared to the steepest descent method and minimal error method. We present an academic example which satisfies the assumptions of this paper. © 2016 Elsevier Inc.
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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.