On the modified iterative methods for $M$-matrix linear systems

Document Type: Research Paper


Department of Mathematics‎, ‎Vali-e-Asr University of Rafsanjan‎, ‎P‎.‎O‎. ‎Box 518‎, ‎Rafsanjan‎, ‎Iran


This paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. Recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the Accelerated Overrelaxation (AOR) method. In this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditions. More precisely, it is demonstrated that the preconditioned Mixed-Type Splitting (MTS) iterative methods can surpass the preconditioned AOR iterative methods for an entirely general class of preconditioners handled by Wang and Song [J. Comput. Appl. Math. 226 (2009), no. 1, 114--124]. Finally some numerical results are elaborated which confirm the validity of the established results.


Main Subjects

Volume 41, Issue 6
November and December 2015
Pages 1519-1535
  • Receive Date: 11 July 2014
  • Revise Date: 04 October 2014
  • Accept Date: 05 October 2014