\input zb-basic \input zb-ioport \iteman{io-port 05813913} \itemau{Wu, Ai-Guo; Feng, Gang; Duan, Guang-Ren; Wu, Wei-Jun} \itemti{Iterative solutions to coupled Sylvester-conjugate matrix equations.} \itemso{Comput. Math. Appl. 60, No. 1, 54-66 (2010).} \itemab Summary: This paper is concerned with iterative solutions to the coupled Sylvester-conjugate matrix equation with a unique solution. By applying a hierarchical identification principle, an iterative algorithm is established to solve this class of complex matrix equations. With a real representation of a complex matrix as a tool, a sufficient condition is given to guarantee that the iterative solutions given by the proposed algorithm converge to the exact solution for any initial matrices. In addition, a sufficient convergence condition that is easier to compute is also given by the original coefficient matrices. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm. \itemrv{~} \itemcc{} \itemut{coupled Sylvester-conjugate matrix equation; iterative algorithm; spectral norm; real representation; convergence} \itemli{doi:10.1016/j.camwa.2010.04.029} \end