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An iterative regularization method for ill-posed Hammerstein type operator equation
(Walter de Gruyter GmbH, 2009) George, S.; Kunhanandan, M.
A combination of Newton's method and a regularization method has been considered for obtaining a stable approximate solution for ill-posed Hammerstein type operator equation. By choosing the regularization parameter according to an adaptive scheme considered by Pereverzev and Schock (2005) an order optimal error estimate has been obtained. Moreover the method that we consider gives quadratic convergence compared to the linear convergence obtained by George and Nair (2008). © de Gruyter 2009.
A two step newton type iteration for ill-posed Hammerstein type operator equations in Hilbert scales
(Rocky Mountain Mathematics Consortium PO Box 871904 Tempe AZ 85287-1804, 2014) Erappa, M.E.; George, S.; Kunhanandan, M.
In this paper regularized solutions of ill-posed Hammerstein type operator equation KF(x) = y, where K : X ? Y is a bounded linear operator with non-closed range and F : X ? X is non-linear, are obtained by a two step Newton type iterative method in Hilbert scales, where the available data is y? in place of actual data y with