M-preconditioner for M-matrices

Linear systems with M-matrices often appear in a wide variety of areas of biological, physical and social sciences, see [A. Berman, R. Plemmons, Nonnegative Matrices in Mathematical Sciences, SIAM Press, Philadelphia, 1994]. In this paper, we propose a preconditioner for solving the system with symmetric nonsingular M-matrix by the preconditioned conjugate gradient (PCG) method. We show that our proconditioner increases the convergence rate of the PCG method and reduces the operation cost. Numerical results are also given.