%0 Journal Article %T Comparison results on the preconditioned mixed-type splitting iterative method for M-matrix linear systems %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Mohseni Moghadam, M. %A Panjeh Ali Beik, Fatemeh %D 2012 %\ 07/15/2012 %V 38 %N 2 %P 349-367 %! Comparison results on the preconditioned mixed-type splitting iterative method for M-matrix linear systems %K Linear systems %K Mixed-type splitting iterative method %K Preconditioned matrix %K M-matrix %R %X Consider the linear system Ax=b where the coefficient matrix A is an M-matrix. In the present work, it is proved that the rate of convergence of the Gauss-Seidel method is faster than the mixed-type splitting and AOR (SOR) iterative methods for solving M-matrix linear systems. Furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a preconditioned matrix. Comparison theorems show that the rate of convergence of the preconditioned Gauss-Seidel method is faster than the preconditioned mixed-type splitting and AOR (SOR) iterative methods. Finally, some numerical examples are presented to illustrate the reality of our comparison theorems. %U http://bims.iranjournals.ir/article_211_dc5b9e9e1b2a179a471b622100c26a58.pdf