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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.
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.