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

Abstract

ABSTRACTFor given symmetric orthogonal matrices R, S, i.e. RT = R, R2 = I, ST = S, S2 = I, a matrix is termed (R, S)-conjugate matrix if . 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.