On Algebraic Structure of Improved Gauss-Seidel Iteration

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dc.contributor.authorBamigbola, Olabode Matthias
dc.contributor.authorIbrahim, Adebisi A.
dc.date.accessioned2019-04-10T13:39:19Z
dc.date.available2019-04-10T13:39:19Z
dc.date.issued2014
dc.descriptionInternational Journal of Mathematical, Computational, Physical and Quantum Engineering 8(10), 1161 - 1166. http://www.waset.org/publication/9999476en_US
dc.description.abstractAnalysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined apriori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss- Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss- Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.en_US
dc.description.sponsorshipTET Fund through the University of Ilorin, Ilorin, Nigeriaen_US
dc.identifier.urihttp://hdl.handle.net/123456789/1719
dc.language.isoenen_US
dc.publisherWorld Academy of Science, Engineering and Technologyen_US
dc.subjectLinear system of equationsen_US
dc.subjectGauss-Seidel iterationen_US
dc.subjectAlgebraic structureen_US
dc.subjectConvergenceen_US
dc.titleOn Algebraic Structure of Improved Gauss-Seidel Iterationen_US
dc.typeArticleen_US

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