On the Accelerated Overrelaxation Method
Pure and Applied Mathematics Journal
Volume 4, Issue 1, February 2015, Pages: 26-31
Received: Dec. 29, 2014; Accepted: Jan. 25, 2015; Published: Feb. 2, 2015
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Authors
I. K. Youssef, Math. Dept. Faculty of Science Ain Shams Uni., Cairo, Egypt
M. M. Farid, Basic Science Dept. British University in Egypt, Elshorouk City, Cairo, Egypt
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Abstract
A new variant of the accelerated over relaxation (AOR) method for solving systems of linear algebraic equations, the KAOR method is established. The treatment depends on the use of the extrapolation techniques introduced by Hadjidimos (1978) and the KSOR introduced by Youssef (2012) and its modified version published in (2013). The KAOR is an extrapolation version of the KSOR. This approach has enables us in establishing eigenvalue functional relations concerning the eigenvalues of the iteration matrices and their spectral radii. Moreover, our eigenvalue functional relation depends directly on the eigenvalues of Jacobi iteration matrix. The proposed method considers the advantages of the AOR in addition to those of the KSOR. A graphical representation of the behavior of the spectral radius near the minimum value illustrates the smoothness in the choice of optimum parameters.
Keywords
SOR, KSOR, AOR, QAOR, KAOR
To cite this article
I. K. Youssef, M. M. Farid, On the Accelerated Overrelaxation Method, Pure and Applied Mathematics Journal. Vol. 4, No. 1, 2015, pp. 26-31. doi: 10.11648/j.pamj.20150401.14
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