On convergence of regularized modified Newton's method for nonlinear ill-posed problems
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Date
2010
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Walter de Gruyter GmbH and Co. KG
Abstract
In this paper we consider regularized modified Newton's method for approximately solving the nonlinear ill-posed problem F(x) = y, where the right hand side is replaced by noisy data y?? Y with y - y?? ? and F : D(F) ? X ? Y is a nonlinear operator between Hilbert spaces X and Y. Under the assumption that Fréchet derivative F? of F is Lipschitz continuous, a choice of the regularization parameter and a stopping rule based on a majorizing sequence are presented. We prove that under a general source condition on , the error between the regularized approximation and the solution of optimal order. © de Gruyter 2010.
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Keywords
Euler equations, Mathematical operators, Numerical methods, Tungsten compounds, Lipschitz continuous, Majorizing sequences, Modified Newton's method, Nonlinear ill-posed problems, Regularization parameters, Regularized approximation, Regularized newton's methods, Tihkonov regularization, Newton-Raphson method
Citation
Journal of Inverse and Ill-Posed Problems, 2010, 18, 2, pp. 133-146