Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38220120715Comparison results on the preconditioned mixed-type splitting
iterative method for M-matrix linear systems349367211ENM.Mohseni MoghadamShahid Bahonar University of KermanFatemehPanjeh Ali BeikVali-Asr University of RafsanjanJournal Article20100903Consider the linear system Ax=b where the coefficient <br />matrix A is an M-matrix. In the present work, it is proved <br />that the rate of convergence of the Gauss-Seidel method is faster <br />than the mixed-type splitting and AOR (SOR) iterative methods for <br />solving M-matrix linear systems. Furthermore, we improve the rate <br />of convergence of the mixed-type splitting iterative method by <br />applying a preconditioned matrix. Comparison theorems show that <br />the rate of convergence of the preconditioned Gauss-Seidel method <br />is faster than the preconditioned mixed-type splitting and AOR <br />(SOR) iterative methods. Finally, some numerical examples are <br />presented to illustrate the reality of our comparison theorems.http://bims.iranjournals.ir/article_211_dc5b9e9e1b2a179a471b622100c26a58.pdf