Faculty Publications
Permanent URI for this communityhttps://idr.nitk.ac.in/handle/123456789/18736
Publications by NITK Faculty
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Item Lavrentiev's regularization method for nonlinear ill-posed equations in Banach spaces(Elsevier B.V., 2018) George, S.; Sreedeep, C.D.In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the implementation of Lavrentiev regularization method. Using 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. © 2018 Wuhan Institute of Physics and MathematicsItem 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 Newton–Kantorovich regularization method for nonlinear ill-posed equations involving m- accretive operators in Banach spaces(Springer springer@springer.it, 2020) Sreedeep, C.D.; George, S.; Argyros, I.K.In this paper, we study nonlinear ill-posed problems involving m- accretive mappings in Banach spaces. We consider Newton–Kantorovich regularization method for the implementation of Lavrentiev regularization method. 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. © 2019, Springer-Verlag Italia S.r.l., part of Springer Nature.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.