*(English)*Zbl 1196.65081

Authorsâ€™ abstract: The generalised coupled Sylvester matrix equations

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 |

15A24 | Matrix equations and identities |

65F10 | Iterative methods for linear systems |