%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