Iterative (, )-conjugate solutions to the generalised coupled Sylvester matrix equations

Sheng-Kun Li

International Journal of Systems Science, 2017, vol. 48, issue 15, 3355-3362

Abstract: For given symmetric orthogonal matrices R, S, i.e. RT = R, R2 = I, ST = S, S2 = I, a matrix A∈Cn×s$A\in \mathbb {C}^{n\times s}$ is termed (R, S)-conjugate matrix if RAS=A‾$RAS=\overline{A}$. In this paper, an iterative method is constructed to find the (R, S)-conjugate solutions of the generalised coupled Sylvester matrix equations. The consistency of the considered matrix equations over (R, S)-conjugate matrices is discussed. When the matrix equations have a unique (R, S)-conjugate solution pair, the proposed method is convergent for any initial (R, S)-conjugate matrix pair under a loose restriction on the convergent factor. Moreover, the optimal convergent factor of the presented method is derived. Finally, some numerical examples are given to illustrate the results and effectiveness.

Date: 2017
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DOI: 10.1080/00207721.2017.1367971

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