TY - JOUR
T1 - Comparison Results Between Preconditioned Jacobi and the <em>AOR</em> Iterative Method
AU -  W. Li & J. C. Li
JO - Numerical Mathematics, a Journal of Chinese Universities
VL - 4
SP - 313
EP - 319
PY - 2007
DA - 2007/11
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/nm/8059.html
KW - 
AB - 
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.