Faculty Publications
Permanent URI for this communityhttps://idr.nitk.ac.in/handle/123456789/18736
Publications by NITK Faculty
Browse
4 results
Search Results
Item Finite dimensional realization of a Guass-Newton method for ill-posed hammerstein type operator equations(2012) Erappa, M.E.; George, S.Finite dimensional realization of an iterative regularization method for approximately solving the non-linear ill-posed Hammerstein type operator equations KF(x) = f, is considered. The proposed method is a combination of the Tikhonov regularization and Guass-Newton method. The advantage of the proposed method is that, we use the Fr chet derivative of F only at one point in each iteration. We derive the error estimate under a general source condition and the regularization parameter is chosen according to balancing principle of Pereverzev and Schock (2005). The derived error estimate is of optimal order and the numerical example provided proves the efficiency of the proposed method. © 2012 Springer-Verlag.Item Dynamical system method for ill-posed Hammerstein type operator equations with monotone operators(2012) Erappa, M.E.; George, S.The problem of approximately solving an ill-posed Hammerstein type operator equation KF(x) = y in a Hilbert space is considered, where K is a bounded linear operator and F is a non-linear monotone operator. The method involves the Dynamical System Method (DSM) - both continuous and iterative schemes, studied by Ramm (2005), and known as Tikhonov regularization. By choosing the regularization parameter according to an adaptive scheme considered by Pereverzev and Schock (2005) an order optimal error estimate has been obtained. © 2012 Academic Publications, Ltd.Item 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 withItem 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.