Vector least-squares solutions for coupled singular matrix equations
The weighted least-squares solutions of coupled singular matrix equations are too difficult to obtain by applying matrices decomposition. In this paper, a family of algorithms are applied to solve these problems based on the Kronecker structures. Subsequently, we construct a computationally efficien...
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| Format: | Article |
| Language: | English English |
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Elsevier
2007
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| Online Access: | http://psasir.upm.edu.my/id/eprint/8687/ http://psasir.upm.edu.my/id/eprint/8687/1/Vector%20least.pdf |
| _version_ | 1848840939423924224 |
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| author | Kilicman, Adem Abdel Aziz Al Zhour, Zeyad |
| author_facet | Kilicman, Adem Abdel Aziz Al Zhour, Zeyad |
| author_sort | Kilicman, Adem |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The weighted least-squares solutions of coupled singular matrix equations are too difficult to obtain by applying matrices decomposition. In this paper, a family of algorithms are applied to solve these problems based on the Kronecker structures. Subsequently, we construct a computationally efficient solutions of coupled restricted singular matrix equations. Furthermore, the need to compute the weighted Drazin and weighted Moore-Penrose inverses; and the use of Tian's work and Lev-Ari's results are due to appearance in the solutions of these problems. The several special cases of these problems are also considered which includes the well-known coupled Sylvester matrix equations. Finally, we recover the iterative methods to the weighted case in order to obtain the minimum D-norm G-vector least-squares solutions for the coupled Sylvester matrix equations and the results lead to the least-squares solutions and invertible solutions, as a special case. © 2006 Elsevier B.V. All rights reserved.
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| first_indexed | 2025-11-15T07:35:18Z |
| format | Article |
| id | upm-8687 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T07:35:18Z |
| publishDate | 2007 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-86872015-09-28T08:24:54Z http://psasir.upm.edu.my/id/eprint/8687/ Vector least-squares solutions for coupled singular matrix equations Kilicman, Adem Abdel Aziz Al Zhour, Zeyad The weighted least-squares solutions of coupled singular matrix equations are too difficult to obtain by applying matrices decomposition. In this paper, a family of algorithms are applied to solve these problems based on the Kronecker structures. Subsequently, we construct a computationally efficient solutions of coupled restricted singular matrix equations. Furthermore, the need to compute the weighted Drazin and weighted Moore-Penrose inverses; and the use of Tian's work and Lev-Ari's results are due to appearance in the solutions of these problems. The several special cases of these problems are also considered which includes the well-known coupled Sylvester matrix equations. Finally, we recover the iterative methods to the weighted case in order to obtain the minimum D-norm G-vector least-squares solutions for the coupled Sylvester matrix equations and the results lead to the least-squares solutions and invertible solutions, as a special case. © 2006 Elsevier B.V. All rights reserved. Elsevier 2007-09-15 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/8687/1/Vector%20least.pdf Kilicman, Adem and Abdel Aziz Al Zhour, Zeyad (2007) Vector least-squares solutions for coupled singular matrix equations. Journal of Computational and Applied Mathematics, 206 (2). pp. 1051-1069. ISSN 0377-0427 http://dx.doi.org/10.1016/j.cam.2006.09.009 10.1016/j.cam.2006.09.009 English |
| spellingShingle | Kilicman, Adem Abdel Aziz Al Zhour, Zeyad Vector least-squares solutions for coupled singular matrix equations |
| title | Vector least-squares solutions for coupled singular matrix equations |
| title_full | Vector least-squares solutions for coupled singular matrix equations |
| title_fullStr | Vector least-squares solutions for coupled singular matrix equations |
| title_full_unstemmed | Vector least-squares solutions for coupled singular matrix equations |
| title_short | Vector least-squares solutions for coupled singular matrix equations |
| title_sort | vector least-squares solutions for coupled singular matrix equations |
| url | http://psasir.upm.edu.my/id/eprint/8687/ http://psasir.upm.edu.my/id/eprint/8687/ http://psasir.upm.edu.my/id/eprint/8687/ http://psasir.upm.edu.my/id/eprint/8687/1/Vector%20least.pdf |