Research Projects

In this project, we will study some simplified versions of two point iterative gradient methods for obtaining stable approximate solution of nonlinear ill-posed operator equations of the form F(x) = y, where F is a nonlinear operator between functional space X and Y. The two point gradient methods available in literature of ill-posed operator equations require calculations of Frechet derivative of the operator F at each iteration step which is computationally a costly process. Thus, we aim to study some simplified variants of these methods. The proposed methods will only require calculation of Frechet derivative of F at the initial guess x_0 of the exact solution. Advantage of use of these simplified versions of the methods is that their numerical complexities are lesser than their classical counter part . For these proposed method, we will do detailed convergence analysis and will also apply these methods to some numerical examples involving parameter identification problem.