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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.

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