## An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation.(English)Zbl 1154.65023

A real matrix A of order $$n$$ is reflexive with respect to a real matrix $$P$$ if $$A=PAP$$, where $$P$$ is symmetric and involutory. An iterative algorithm for the generalized coupled Sylvester matrix equations over reflexive matrices is considered. The method is used to obtain a reflexive solution pair and under certain conditions the least Frobenius norm reflexive solution pair can also be computed. Some examples illustrate the presentation.

### MSC:

 65F30 Other matrix algorithms (MSC2010) 15A24 Matrix equations and identities
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### References:

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