Approximation of iteration number for Gauss-Seidel using Redlich-Kister polynomial
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) a...
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| Format: | Article |
| Language: | English |
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Science Publications
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/13257/ http://psasir.upm.edu.my/id/eprint/13257/1/ajassp.2010.969.975.pdf |
| _version_ | 1848842063462793216 |
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| author | Hasan, Mohammad Khatim Sulaiman, Jumat Ahmad, S. Othman, Mohamed Abdul Karim, Samsul Ariffin |
| author_facet | Hasan, Mohammad Khatim Sulaiman, Jumat Ahmad, S. Othman, Mohamed Abdul Karim, Samsul Ariffin |
| author_sort | Hasan, Mohammad Khatim |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-15T07:53:10Z |
| format | Article |
| id | upm-13257 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T07:53:10Z |
| publishDate | 2010 |
| publisher | Science Publications |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-132572017-11-27T08:44:02Z http://psasir.upm.edu.my/id/eprint/13257/ Approximation of iteration number for Gauss-Seidel using Redlich-Kister polynomial Hasan, Mohammad Khatim Sulaiman, Jumat Ahmad, S. Othman, Mohamed Abdul Karim, Samsul Ariffin 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. Science Publications 2010 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/13257/1/ajassp.2010.969.975.pdf Hasan, Mohammad Khatim and Sulaiman, Jumat and Ahmad, S. and Othman, Mohamed and Abdul Karim, Samsul Ariffin (2010) Approximation of iteration number for Gauss-Seidel using Redlich-Kister polynomial. American Journal of Applied Sciences, 7 (7). pp. 969-975. ISSN 1546-9239; ESSN: 1554-3641 http://thescipub.com/abstract/10.3844/ajassp.2010.969.975 10.3844/ajassp.2010.969.975 |
| spellingShingle | Hasan, Mohammad Khatim Sulaiman, Jumat Ahmad, S. Othman, Mohamed Abdul Karim, Samsul Ariffin Approximation of iteration number for Gauss-Seidel using Redlich-Kister polynomial |
| title | Approximation of iteration number for Gauss-Seidel using Redlich-Kister polynomial |
| title_full | Approximation of iteration number for Gauss-Seidel using Redlich-Kister polynomial |
| title_fullStr | Approximation of iteration number for Gauss-Seidel using Redlich-Kister polynomial |
| title_full_unstemmed | Approximation of iteration number for Gauss-Seidel using Redlich-Kister polynomial |
| title_short | Approximation of iteration number for Gauss-Seidel using Redlich-Kister polynomial |
| title_sort | approximation of iteration number for gauss-seidel using redlich-kister polynomial |
| url | http://psasir.upm.edu.my/id/eprint/13257/ http://psasir.upm.edu.my/id/eprint/13257/ http://psasir.upm.edu.my/id/eprint/13257/ http://psasir.upm.edu.my/id/eprint/13257/1/ajassp.2010.969.975.pdf |