Approximation of iteration number for Gauss-Seidel using Redlich-Kister polynomial

Hasan, M.K. and Sulaiman, J. and Ahmad, S. and Othman, Mohamed and Karim, S.A.A. (2010) Approximation of iteration number for Gauss-Seidel using Redlich-Kister polynomial. American Journal of Applied Sciences, 7 (7). pp. 956-962. ISSN 1546-9239

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Abstract

Problem statement: Development of mathematical models based on set of observed data plays a crucial role to describe and predict any phenomena in science, engineering and economics. Therefore, the main purpose of this study was to compare the efficiency of Arithmetic Mean (AM), Geometric Mean (GM) and Explicit Group (EG) iterative methods to solve system of linear equations via estimation of unknown parameters in linear models. Approach: The system of linear equations for linear models generated by using least square method based on (m+1) set of observed data for number of Gauss-Seidel iteration from various grid sizes. Actually there were two types of linear models considered such as piece-wise linear polynomial and piece-wise Redlich-Kister polynomial. All unknown parameters of these models estimated and calculated by using three proposed iterative methods. Results: Thorough several implementations of numerical experiments, the accuracy for formulations of two proposed models had shown that the use of the third-order Redlich-Kister polynomial has high accuracy compared to linear polynomial case. Conclusion: The efficiency of AM and GM iterative methods based on the Redlich-Kister polynomial is superior as compared to EG iterative method.

Item Type:Article
Keyword:Arithmetic mean; Geometric mean; Explicit group; Redlich-Kister model; Poisson equation
Subject:Iterative methods (Mathematics)
Subject:Electronic data processing
Subject:Computer algorithms
Faculty or Institute:Faculty of Computer Science and Information Technology
Publisher:Science Publications
ID Code:13257
Deposited By: Umikalthom Abdullah
Deposited On:28 Mar 2012 02:02
Last Modified:19 Dec 2012 08:03

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