Generalized conjugate direction algorithm for solving generalized coupled Sylvester transpose matrix equations over reflexive or anti-reflexive matrices
The paper studies the iterative solutions of the generalized coupled Sylvester transpose matrix equations over the reflexive (anti-reflexive) matrix group by the generalized conjugate direction algorithm. The convergence analysis shows that the solution group can be obtained within finite iterative...
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| Published in | Journal of the Franklin Institute Vol. 359; no. 13; pp. 6958 - 6985 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.09.2022
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| Online Access | Get full text |
| ISSN | 0016-0032 1879-2693 |
| DOI | 10.1016/j.jfranklin.2022.07.005 |
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| Abstract | The paper studies the iterative solutions of the generalized coupled Sylvester transpose matrix equations over the reflexive (anti-reflexive) matrix group by the generalized conjugate direction algorithm. The convergence analysis shows that the solution group can be obtained within finite iterative steps in the absence of round-off errors for any initial given reflexive (anti-reflexive) matrix group. Furthermore, we can get the minimum-norm solution group by choosing special kinds of initial matrix group. Finally, some numerical examples are given to demonstrate the algorithm considered is quite effective in actual computation. |
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| AbstractList | The paper studies the iterative solutions of the generalized coupled Sylvester transpose matrix equations over the reflexive (anti-reflexive) matrix group by the generalized conjugate direction algorithm. The convergence analysis shows that the solution group can be obtained within finite iterative steps in the absence of round-off errors for any initial given reflexive (anti-reflexive) matrix group. Furthermore, we can get the minimum-norm solution group by choosing special kinds of initial matrix group. Finally, some numerical examples are given to demonstrate the algorithm considered is quite effective in actual computation. |
| Author | Hu, Jingjing Ma, Changfeng Ke, Yifen |
| Author_xml | – sequence: 1 givenname: Jingjing surname: Hu fullname: Hu, Jingjing – sequence: 2 givenname: Yifen surname: Ke fullname: Ke, Yifen email: keyifen@fjnu.edu.cn – sequence: 3 givenname: Changfeng surname: Ma fullname: Ma, Changfeng email: macf@fjnu.edu.cn |
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