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

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.

Keywords:

• coupled Sylvester-transpose matrix equations
• iterative algorithm
• generalized centro-symmetric matrix

2010 AMS Subject Classifications:

• 15A24
• 65F10

Acknowledgements

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