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.


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