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Volume 10, Issue 4
Optimum Modified SOR (MSOR) Method in a Special Case

A. K. Yeyios

J. Comp. Math., 10 (1992), pp. 358-365.

Published online: 1992-10

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  • Abstract

In this paper we study the MSOR method with fixed parameters, when applied to a linear system of equations $Ax=b(1)$, where $A$ is consistently ordered and all the eigenvalues of the iteration matrix of the Jacobi method for (1) are purely imaginary. The optimum parameters and the optimum virtual spectral radius of the MSOR method are also obtained by an analysis similar to that of [5, pp. 277-281] for the real case. Finally, a comparison of the optimum MSOR method with the optimum SOR and AOR methods is presented, showing the superiority of the MSOR one.

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@Article{JCM-10-358, author = {A. K. Yeyios}, title = {Optimum Modified SOR (MSOR) Method in a Special Case}, journal = {Journal of Computational Mathematics}, year = {1992}, volume = {10}, number = {4}, pages = {358--365}, abstract = {

In this paper we study the MSOR method with fixed parameters, when applied to a linear system of equations $Ax=b(1)$, where $A$ is consistently ordered and all the eigenvalues of the iteration matrix of the Jacobi method for (1) are purely imaginary. The optimum parameters and the optimum virtual spectral radius of the MSOR method are also obtained by an analysis similar to that of [5, pp. 277-281] for the real case. Finally, a comparison of the optimum MSOR method with the optimum SOR and AOR methods is presented, showing the superiority of the MSOR one.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9368.html} }
TY - JOUR T1 - Optimum Modified SOR (MSOR) Method in a Special Case AU - A. K. Yeyios JO - Journal of Computational Mathematics VL - 4 SP - 358 EP - 365 PY - 1992 DA - 1992/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9368.html KW - AB -

In this paper we study the MSOR method with fixed parameters, when applied to a linear system of equations $Ax=b(1)$, where $A$ is consistently ordered and all the eigenvalues of the iteration matrix of the Jacobi method for (1) are purely imaginary. The optimum parameters and the optimum virtual spectral radius of the MSOR method are also obtained by an analysis similar to that of [5, pp. 277-281] for the real case. Finally, a comparison of the optimum MSOR method with the optimum SOR and AOR methods is presented, showing the superiority of the MSOR one.

A. K. Yeyios. (1992). Optimum Modified SOR (MSOR) Method in a Special Case. Journal of Computational Mathematics. 10 (4). 358-365. doi:
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