## 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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### References:

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