Modified iterative methods for nonnegative matrices and M-matrices linear systems

The purpose of this paper is to present new preconditioning techniques for solving nonnegative matrices linear system and M-matrices linear system Ax = b based on the I + S(@a) type preconditioning matrices provided by Hadjidimos et al.^[^1^] and Evans et al.^[^2^]. Convergence analysis of the proposed methods are given. Numerical results are presented, which show the improvements on the convergence rate of the Jacobi type and Gauss-Seidel type preconditioned iterative methods.