A New Version of the Accelerated Overrelaxation Iterative Method
Hadjidimos (1978) proposed a classical accelerated overrelaxation (AOR) iterative method to solve the system of linear equations, and discussed its convergence under the conditions that the coefficient matrices are irreducible diagonal dominant, L-matrices, and consistently orders matrices. In this...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/725360 |
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| author | Shi-Liang Wu Yu-Jun Liu |
| author_facet | Shi-Liang Wu Yu-Jun Liu |
| author_sort | Shi-Liang Wu |
| collection | DOAJ |
| description | Hadjidimos (1978) proposed a classical accelerated overrelaxation (AOR) iterative method to solve the system of linear equations, and discussed its convergence under the conditions that the coefficient matrices are irreducible diagonal dominant, L-matrices, and consistently orders matrices. In this paper, a new version of the AOR method is presented. Some convergence results are derived when the coefficient matrices are irreducible diagonal dominant, H-matrices, symmetric positive definite matrices, and L-matrices. A relational graph for the new AOR method and the original AOR method is presented. Finally, a numerical example is presented to illustrate the efficiency of the proposed method. |
| format | Article |
| id | doaj-art-4bbc304f142a40b68a2040b46e51ab89 |
| institution | DOAJ |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4bbc304f142a40b68a2040b46e51ab892025-08-20T03:20:13ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/725360725360A New Version of the Accelerated Overrelaxation Iterative MethodShi-Liang Wu0Yu-Jun Liu1School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, ChinaSchool of Mathematics and Statistics, Anyang Normal University, Anyang 455000, ChinaHadjidimos (1978) proposed a classical accelerated overrelaxation (AOR) iterative method to solve the system of linear equations, and discussed its convergence under the conditions that the coefficient matrices are irreducible diagonal dominant, L-matrices, and consistently orders matrices. In this paper, a new version of the AOR method is presented. Some convergence results are derived when the coefficient matrices are irreducible diagonal dominant, H-matrices, symmetric positive definite matrices, and L-matrices. A relational graph for the new AOR method and the original AOR method is presented. Finally, a numerical example is presented to illustrate the efficiency of the proposed method.http://dx.doi.org/10.1155/2014/725360 |
| spellingShingle | Shi-Liang Wu Yu-Jun Liu A New Version of the Accelerated Overrelaxation Iterative Method Journal of Applied Mathematics |
| title | A New Version of the Accelerated Overrelaxation Iterative Method |
| title_full | A New Version of the Accelerated Overrelaxation Iterative Method |
| title_fullStr | A New Version of the Accelerated Overrelaxation Iterative Method |
| title_full_unstemmed | A New Version of the Accelerated Overrelaxation Iterative Method |
| title_short | A New Version of the Accelerated Overrelaxation Iterative Method |
| title_sort | new version of the accelerated overrelaxation iterative method |
| url | http://dx.doi.org/10.1155/2014/725360 |
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