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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.