Abstract

For a given symmetric orthogonal matrix R, i.e., RT = R, R2 = I, a matrix A ? Cnxn is termed Hermitian R-conjugate matrix if A = AH, RAR = ?. In this paper, an iterative method is constructed for finding the Hermitian R-conjugate solutions of general coupled Sylvester matrix equations. Convergence analysis shows that when the considered matrix equations have a unique solution group then the proposed method is always convergent for any initial Hermitian R-conjugate matrix group under a loose restriction on the convergent factor. Furthermore, the optimal convergent factor is derived. Finally, two numerical examples are given to demonstrate the theoretical results and effectiveness.

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