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 precond...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.展开更多
基金The work was supported by Xi'an Jiaotong University Natural Science Foundation, China.
文摘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.
