On the reflexive and anti-reflexive solutions of the generalised coupled Sylvester matrix equations. (English) Zbl 1196.65081

Authors’ abstract: The generalised coupled Sylvester matrix equations
\[ \begin{aligned} AXB + CYD &= J\\ EXF+GYH&=K,\end{aligned} \]
with unknown matrices \(X\) and \(Y\), have important applications in control and system theory. Also, it is well known that reflexive and anti-reflexive matrices have wide applications in many fields. In this article, we consider the generalised coupled Sylvester matrix equations over reflexive and anti-reflexive matrices. First we propose two new matrix equations equivalent to the generalised coupled Sylvester matrix equations over reflexive and anti-reflexive matrices, respectively. Then, two new iterative algorithms are proposed for solving these matrix equations. A convergence analysis of the proposed iterative algorithms is derived. Finally, some numerical examples are presented to illustrate the theoretical results of this article.


65F30 Other matrix algorithms (MSC2010)
15A24 Matrix equations and identities
65F10 Iterative numerical methods for linear systems
Full Text: DOI


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