182
Views
21
CrossRef citations to date
0
Altmetric
Section B

The coupled Sylvester-transpose matrix equations over generalized centro-symmetric matrices

&
Pages 1546-1566 | Received 12 Apr 2012, Accepted 17 Dec 2012, Published online: 19 Mar 2013
 

Abstract

In this paper, we present an iterative algorithm for solving the following coupled Sylvester-transpose matrix equations

over the generalized centro-symmetric matrix group (X 1, X 2, …, X q ). The solvability of the problem can be determined by the proposed algorithm, automatically. If the coupled Sylvester-transpose matrix equations are consistent over the generalized centro-symmetric matrices, then a generalized centro-symmetric solution group can be obtained within finite iterative steps for any initial generalized centro-symmetric matrix group in the exact arithmetic. Furthermore, it is shown that the least-norm generalized centro-symmetric solution group of the coupled Sylvester-transpose matrix equations can be computed by choosing an appropriate initial iterative matrix group. Moreover, the optimal approximate generalized centro-symmetric solution group to a given arbitrary matrix group (V 1, V 2, …, V q ) can be derived by finding the least-norm generalized centro-symmetric solution group of a new coupled Sylvester-transpose matrix equations. Finally, some numerical results are given to illustrate the validity and practicability of the theoretical results established in this work.

2010 AMS Subject Classifications:

Acknowledgements

The authors appreciate the anonymous referees for their helpful comments and recommendations which improved the quality of the paper.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.