Comparison Results Between Preconditioned Jacobi and the AOR Iterative Method

摘要

The large scale linear systems with M-matrices often appear in a wide variety of areas of physical,fluid dynamics and economic sciences.It is reported in[1]that the convergence rate of the IMGS method,with the preconditioner I+S_α,is superior to that of the basic SOR iterative method for the M-matrix.This paper considers the preconditioned Jacobi(PJ)method with the preconditioner P=I+S_α+S_β,and proves theoretically that the convergence rate of the PJ method is better than that of the basic AOR method.Numerical examples are provided to illustrate the main results obtained.