Preconditioning technique for symmetric M-matrices

Linear systems with M -matrices occur in a wide variety of areas including numerical partial differential equations, input-output production and growth models in economics, linear complementarity problems in operations research and Markov chains in stochastic analysis. In this paper, we propose a new preconditioner for solving a system with symmetric positive definite M -matrix by the preconditioned conjugate gradient (PCG) method. We show that our preconditioner increases the convergence rate of the PCG method and reduces the operation cost. Numerical results are given. [PUBLICATION ABSTRACT]