Preconditioned Rrgmres For Discrete Ill-Posed Problems

Range Restricted GMRES (RRGMRES) can be considered as regularizing iterative method and its iterates as regularized solutions. In this paper, we use two preconditioned versions of this method for solving ill-posed inverse problems. Our proposed preconditioner matrix is appropriate to use directly for linear systems of the form Ax = b with square ill-conditioned coefficient matrix. We show numerically that the Preconditioned RRGMRES method has more stable solution compared to RRGMRES.