The 3-Block KSOR Method for Full Rank Rectangular Systems
Pure and Applied Mathematics Journal
Volume 5, Issue 4, August 2016, Pages: 103-107
Received: May 24, 2016; Accepted: Jun. 2, 2016; Published: Jun. 21, 2016
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Authors
I. K. Youssef, Math Department, Faculty of Science, Ain Shams University, Cairo, Abbassia, Egypt
Salwa M. Ali, Math Department, Faculty of Science, Ain Shams University, Cairo, Abbassia, Egypt
M. A. Naser, Math Department, Faculty of Science, Ain Shams University, Cairo, Abbassia, Egypt
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Abstract
A new version of the KSOR method is considered to introduce the least squares solution of a full rank over determinant system of linear algebraic equations. The treatment depends on introducing an augmented non-singular square system through splitting the coefficient matrix A into two matrices A1, A2 with non-singular part, A1. Accordingly, a new version of the 3-block SOR method is introduced, the 3-block KSOR method. Selection of the relaxation parameter which guarantees the convergence in the sense of reducing the spectral radius of the iteration matrix is considered. Application of the theoretical results to a numerical example has confirmed the expected behaviour of the 3-block KSOR method.
Keywords
SOR, KSOR, 3 Block SOR Method, Rectangular Systems
To cite this article
I. K. Youssef, Salwa M. Ali, M. A. Naser, The 3-Block KSOR Method for Full Rank Rectangular Systems, Pure and Applied Mathematics Journal. Vol. 5, No. 4, 2016, pp. 103-107. doi: 10.11648/j.pamj.20160504.13
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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