Simplified Landweber scheme for nonlinear ill-posed problems.

Abstract :Landweber iterative method is one of the techniques used for solving nonlinear ill-posed problems. The convergence of the scheme and error estimate are usually derived with many assumptions which is very diffi cult to verify from a practical point of view. In this talk, we consider a simplied form of Landweber iterative scheme for solving nonlinear ill- posed problems. We derive the convergence analysis and error estimate using weaker assumptions. The Landweber method is considered as a regularization scheme when the iteration is stopped at the appropriate stage using the discrepancy principle. We use the discrepancy principle used in standard scheme for stopping the iteration scheme. We supply the numerical results to illustrate the above features.