Gradient-based iterative algorithms for generalized coupled Sylvester-conjugate matrix equations

By applying the hierarchical identification principle, the gradient-based iterative algorithm is suggested to solve a class of complex matrix equations. With the real representation of a complex matrix as a tool, the sufficient and necessary conditions for the convergence factor are determined to guarantee that the iterative solutions given by the proposed algorithm converge to the exact solution for any initial matrices. Also, we solve the problem which is proposed by Wu et al. (2010). Finally, some numerical examples are provided to illustrate the effectiveness of the proposed algorithms and testify the conclusions suggested in this paper.