A Note on the GMRES Method for Linear Discrete Ill-Posed Problems

Abstract. In this paper, we are presenting a proposal for new modified algorithms for RRGMRES and AGMRES. It is known that RRGMRES and AGMRES are viable methods for solving linear discrete ill-posed problems. In this paper we have fo-cused on the residual norm and have come-up with two improvements where suc-cessive updates and the stabilization of decreases for the residual norm improve performance respectively. Our numerical experiments confirm that our improved algorithms are effective for linear discrete ill-posed problems