Volume 16, Issue 4
Comparison Results Between Preconditioned Jacobi and the AOR Iterative Method

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 16 (2007), pp. 313-319

• Abstract

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 $I+S_{\alpha}$, 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 $P=I+S_{\alpha}+S_{\beta}$, 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.

• History

Accepted:

Published online: 2007-11

• Keywords