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

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.