@Article{NM-16-313, author = { W. Li and J. C. Li}, title = {Comparison Results Between Preconditioned Jacobi and the AOR Iterative Method}, journal = {Numerical Mathematics, a Journal of Chinese Universities}, year = {2007}, volume = {16}, number = {4}, pages = {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.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/8059.html} }