Browsing by Author "Kanagaraj, K."

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    Derivative Free Regularization Method for Nonlinear Ill-Posed Equations in Hilbert Scales
    (2018) George, S.; Kanagaraj, K.
    In this paper, we deal with nonlinear ill-posed operator equations involving a monotone operator in the setting of Hilbert scales. Our convergence analysis of the proposed derivative-free method is based on the simple property of the norm of a self-adjoint operator. Using a general H lder-type source condition, we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) for choosing the regularization parameter. Finally, we applied the proposed method to the parameter identification problem in an elliptic PDE in the setting of Hilbert scales and compare the results with the corresponding method in Hilbert space. 2018 Walter de Gruyter GmbH, Berlin/Boston 2018.
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    Derivative free regularization method for nonlinear ill-posed equations in Hilbert scales
    (De Gruyter Open Ltd, 2019) George, S.; Kanagaraj, K.
    In this paper, we deal with nonlinear ill-posed operator equations involving a monotone operator in the setting of Hilbert scales. Our convergence analysis of the proposed derivative-free method is based on the simple property of the norm of a self-adjoint operator. Using a general Hölder-type source condition, we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) for choosing the regularization parameter. Finally, we applied the proposed method to the parameter identification problem in an elliptic PDE in the setting of Hilbert scales and compare the results with the corresponding method in Hilbert space. © 2019 De Gruyter. All rights reserved.
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    Discrepancy principles for fractional Tikhonov regularization method leading to optimal convergence rates
    (2019) Kanagaraj, K.; Reddy, G.D.; George, S.
    Fractional Tikhonov regularization (FTR) method was studied in the last few years for approximately solving ill-posed problems. In this study we consider the Schock-type discrepancy principle for choosing the regularization parameter in FTR and obtained the order optimal convergence rate. Numerical examples are provided in this study. 2019, Korean Society for Informatics and Computational Applied Mathematics.
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    Discrepancy principles for fractional Tikhonov regularization method leading to optimal convergence rates
    (Springer, 2020) Kanagaraj, K.; Reddy, G.D.; George, S.
    Fractional Tikhonov regularization (FTR) method was studied in the last few years for approximately solving ill-posed problems. In this study we consider the Schock-type discrepancy principle for choosing the regularization parameter in FTR and obtained the order optimal convergence rate. Numerical examples are provided in this study. © 2019, Korean Society for Informatics and Computational Applied Mathematics.
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    Local convergence analysis of two iterative methods
    (Springer Science and Business Media B.V., 2022) George, S.; Argyros, I.K.; Senapati, K.; Kanagaraj, K.
    In this paper we consider two three-step iterative methods with common first two steps. The convergence order five and six, respectively of these methods are proved using assumptions on the first derivative of the operator involved. We also provide dynamics of these methods © 2022, The Author(s), under exclusive licence to The Forum D’Analystes.