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
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Official URL: http://dx.doi.org/10.1016/j.cam.2006.09.009
Abstract
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.
| Item Type: | Article |
|---|---|
| Keyword: | Generalized inverses, Iterative methods, Kronecker products, Matrix least-squares problems, Matrix norms |
| Faculty or Institute: | Institute for Mathematical Research |
| Publisher: | Elsevier |
| DOI Number: | 10.1016/j.cam.2006.09.009 |
| ID Code: | 8687 |
| Deposited By: | Erni Suraya Abdul Aziz |
| Deposited On: | 09 Dec 2010 07:20 |
| Last Modified: | 09 Dec 2010 07:31 |
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