In this paper, the generalized Sylvester matrix equation AV + BW = EVF + C over reflexive
matrices is considered. An iterative algorithm for obtaining reflexive solutions of this
matrix equation is introduced. When this matrix equation is consistent over reflexive
solutions then for any initial reflexive matrix, the solution can be obtained within finite
iteration steps. Furthermore, the complexity and the convergence analysis for the
proposed algorithm are given. The least Frobenius norm reflexive solutions can also be
obtained when special initial reflexive matrices are chosen. Finally, numerical examples
are given to illustrate the effectiveness of the proposed algorithm.