Iterative algorithms for coupled Sylvester-conjugate-transpose matrix equations by using hierarchical identification principle

Iterative approaches to solve a class of coupled Sylvester-conjugate-transpose matrix equations with a unique solution are investigated. By applying hierarchical identification principle, an iterative algorithm is proposed to solve this class of complex matrix equations. By using the real representation of a complex matrix, a range of the convergence factor is given such that the proposed algorithm is convergent. By simplification, a sufficient condition guaranteeing the convergence of the proposed algorithm is also given in terms of the original coefficient matrices.