A Simplified Landweber Iteration for Solving Nonlinear Ill-Posed Problems

Landweber iterative method is one of the well-known techniques used for solving nonlinear ill-posed problems. The convergence analysis and error estimates are usually derived with many assumptions which are very difficult to verify from a practical point of view. In this paper, we consider a simplified 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 same discrepancy principle that is used in the standard scheme for stopping the proposed iterative scheme. We supply the numerical results to illustrate the above features. Further, we compare the numerical results of the proposed method with the standard approach and demonstrate that our scheme is stable and achieves good computational output. © 2017, Springer (India) Private Ltd.