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Iterative regularization methods for nonlinear ill-posed operator equations with m-accretive mappings in banach spaces
(Elsevier B.V., 2015) Argyros, I.K.; George, S.
In this paper, a modified Newton type iterative method is considered for approximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping. © 2015 Wuhan Institute of Physics and Mathematics.
Iterative regularization methods for ill-posed operator equations in Hilbert scales
(Cambridge Scientific Publishers jonathan.mckenna@touchbriefings.com, 2017) Argyros, I.K.; George, S.; Padikkal, P.
In this paper we report on a method for regularizing a nonlinear ill-posed operator equation in Hilbert scales. The proposed method is a combination of Lavrentiev regularization method and a Modified Newton's method in Hilbert scales . Under the assumptions that the operator F is continu- ously differentiable with a Lipschitz-continuous first derivative and that the solution of (1.1) fulfils a general source condition, we give an optimal order convergence rate result with respect to the general source function. © CSP - Cambridge, UK; I & S - Florida, USA, 2017.