Faculty Publications

Publications by NITK Faculty

Browse

Now showing 1 - 2 of 2

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
Newton type iteration for Tikhonov regularization of non-linear ill-posed Hammerstein type equations
(2014) George, S.; Erappa, M.E.
An iterative method is investigated for a nonlinear ill-posed Hammerstein type operator equation KF(x)=f. We use a center-type Lipschitz condition in our convergence analysis instead of the usual Lipschitz condition. The adaptive method of Pereverzev and Schock (SIAM J. Numer. Anal. 43(5):2060-2076, 2005) is used for choosing the regularization parameter. The optimality of this method is proved under a general source condition involving the Fréchet derivative of F at some initial guess x 0. A numerical example of nonlinear integral equation shows the efficiency of this procedure. © 2013 Korean Society for Computational and Applied Mathematics.