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

W. Li & J. C. Li

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

Published online: 2007-11

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  • 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.
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@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} }
TY - JOUR T1 - Comparison Results Between Preconditioned Jacobi and the AOR 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.
W. Li & J. C. Li. (1970). Comparison Results Between Preconditioned Jacobi and the AOR Iterative Method. Numerical Mathematics, a Journal of Chinese Universities. 16 (4). 313-319. doi:
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