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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 Mathematics
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.