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February 2009 One Step Closer to an Optimal Two-Parameter SOR Method: A Geometric Approach
Saadat Moussavi
Missouri J. Math. Sci. 21(1): 56-64 (February 2009). DOI: 10.35834/mjms/1316032681


The well-known SOR method is obtained from a one-part splitting of the system matrix $A$, using one parameter $\omega$ for the diagonal. A strong interest in using more than one parameter for the SOR method to improve the convergence has been developed. Sisler, Niethammer, and Hadiidimos worked on the two-parameter method in the seventies. This author has generalized Sisler's method and introduced a range for the second parameter, providing a faster two-parameter method compared to the SOR method. In this paper, we go one step further by removing the hypothesis that requires the eigenvalues of the Jacobi iteration matrix to be real. The result is an optimal value for the second parameter when the eigenvalues of the SOR method are in a certain well-defined region.


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Saadat Moussavi. "One Step Closer to an Optimal Two-Parameter SOR Method: A Geometric Approach." Missouri J. Math. Sci. 21 (1) 56 - 64, February 2009.


Published: February 2009
First available in Project Euclid: 14 September 2011

zbMATH: 1172.65016
MathSciNet: MR2503816
Digital Object Identifier: 10.35834/mjms/1316032681

Primary: 65F10

Rights: Copyright © 2009 Central Missouri State University, Department of Mathematics and Computer Science


Vol.21 • No. 1 • February 2009
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