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

作者：Li, Sheng-Kun^*

来源：International Journal of Systems Science, 2017, 48(15): 3355-3362.

DOI：10.1080/00207721.2017.1367971

• Iterative method
• (R, S)-conjugate matrix
• coupled Sylvester matrix equations

For given symmetric orthogonal matrices R, S, i.e. R-T = R, R-2 = I, S-T = S, S-2 = I, a matrix A is an element of C-nxs is termed (R, S)-conjugate matrix if RAS = (A) over bar. 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.

• 出版日期2017
• 单位成都信息工程大学