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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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