An iteration method with relaxation parameter for solving ill-posed linear operator equations

Abstract In this study, we introduce an iterated regularization method with a relaxation parameter to compute solutions to ill-posed linear operator equations of the first kind, specifically within the framework of bounded operators. The proposed method is accompanied by a comprehensive regularization theory that establishes its stability and convergence. In addition, we derive convergence results and implement effective stopping criteria based on Morozov’s discrepancy principle. Numerical experiments are performed to validate effectiveness of the iterated regularization method and demonstrate its applicability to deblurring problems.