TY - JOUR ID - 211 TI - Comparison results on the preconditioned mixed-type splitting iterative method for M-matrix linear systems JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Mohseni Moghadam, M. AU - Panjeh Ali Beik, Fatemeh AD - Shahid Bahonar University of Kerman AD - Vali-Asr University of Rafsanjan Y1 - 2012 PY - 2012 VL - 38 IS - 2 SP - 349 EP - 367 KW - Linear systems KW - Mixed-type splitting iterative method KW - Preconditioned matrix KW - M-matrix DO - N2 - 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. UR - http://bims.iranjournals.ir/article_211.html L1 - http://bims.iranjournals.ir/article_211_dc5b9e9e1b2a179a471b622100c26a58.pdf ER -