Faculty Publications
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Publications by NITK Faculty
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Item Extended Newton-type iteration for nonlinear ill-posed equations in Banach space(Springer Verlag service@springer.de, 2019) Sreedeep, C.D.; George, S.; Argyros, I.K.In this paper, we study nonlinear ill-posed equations involving m-accretive mappings in Banach spaces. We produce an extended Newton-type iterative scheme that converges cubically to the solution which uses assumptions only on the first Fréchet derivative of the operator. Using general Hölder type source condition we obtain an error estimate. We also use the adaptive parameter choice strategy proposed by Pereverzev and Schock (SIAM J Numer Anal 43(5):2060–2076, 2005) for choosing the regularization parameter. © 2018, Korean Society for Computational and Applied Mathematics.Item 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.Item Secant-type iteration for nonlinear ill-posed equations in Banach space(De Gruyter Open Ltd, 2023) George, S.; Sreedeep, C.D.; Argyros, I.K.In this paper, we study secant-type iteration for nonlinear ill-posed equations involving m-accretive mappings in Banach spaces. We prove that the proposed iterative scheme has a convergence order at least 2.20557 using assumptions only on the first Fréchet derivative of the operator. Further, using a general Hölder-type source condition, we obtain an optimal error estimate. We also use the adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) for choosing the regularization parameter. © 2022 Walter de Gruyter GmbH, Berlin/Boston 2023.