Convergence analysis of the modified sor (MSOR) method

Abstract

In this paper we present an analysis of the convergence of the MSOR method with fixed parameters, for solving a linear system of equations Ax=b, where A belongs to a subclass of consistently ordered matrices. The optimum parameters and the optimum virtual spectral radius of the MSOR method are also obtained. These results extend those of Young [5, pp. 277-281]. Finally, a comparison of the optimum MSOR with the optimum SOR and AOR methods is made, showing the superiority of MSOR.

Keywords:

• Successive overrelaxation (SOR) method
• modified SOR method
• accelerated over- relaxation (AOR) method
• consistently ordered matrices
• virtual spectral radius
• strong convergence

Subject Classifications AMS(MOS):

• 65F10