Convergence analysis of the two preconditioned iterative methods for M-matrix linear systems

In this paper, we present the two preconditioners I+Sˆ and I+Sˆ+R for solving M-matrix linear systems and discuss the convergence of the two preconditioned iterative methods. Meanwhile, we obtain comparison theorems between the two preconditioned iterative methods and consider the solution of M-matrix linear systems by preconditioned Krylov subspace methods. Numerical experiments are given to validate the performance of the preconditioners.