Convergence Results on Iteration Algorithms to Linear Systems
In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most im...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/273873 |
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| author | Zhuande Wang Chuansheng Yang Yubo Yuan |
| author_facet | Zhuande Wang Chuansheng Yang Yubo Yuan |
| author_sort | Zhuande Wang |
| collection | DOAJ |
| description | In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of the Jacobi iterative matrix is positive and the one of backward iterative matrix is strongly positive (lager than a positive constant). Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously). Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods. |
| format | Article |
| id | doaj-art-aa78595e54694cc3a73a4a7611ead606 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-aa78595e54694cc3a73a4a7611ead6062025-02-03T01:21:43ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/273873273873Convergence Results on Iteration Algorithms to Linear SystemsZhuande Wang0Chuansheng Yang1Yubo Yuan2School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaDepartment of Mathematics, Zhejiang Ocean University, Zhoushan, Zhejiang 316000, ChinaSchool of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, ChinaIn order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of the Jacobi iterative matrix is positive and the one of backward iterative matrix is strongly positive (lager than a positive constant). Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously). Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods.http://dx.doi.org/10.1155/2014/273873 |
| spellingShingle | Zhuande Wang Chuansheng Yang Yubo Yuan Convergence Results on Iteration Algorithms to Linear Systems The Scientific World Journal |
| title | Convergence Results on Iteration Algorithms to Linear Systems |
| title_full | Convergence Results on Iteration Algorithms to Linear Systems |
| title_fullStr | Convergence Results on Iteration Algorithms to Linear Systems |
| title_full_unstemmed | Convergence Results on Iteration Algorithms to Linear Systems |
| title_short | Convergence Results on Iteration Algorithms to Linear Systems |
| title_sort | convergence results on iteration algorithms to linear systems |
| url | http://dx.doi.org/10.1155/2014/273873 |
| work_keys_str_mv | AT zhuandewang convergenceresultsoniterationalgorithmstolinearsystems AT chuanshengyang convergenceresultsoniterationalgorithmstolinearsystems AT yuboyuan convergenceresultsoniterationalgorithmstolinearsystems |