A finite iterative method for solving the generalized Hamiltonian solutions of coupled Sylvester matrix equations with conjugate transpose

For given skew- Hermitian unitary matrix J, i. e. J = -J(H), J(H)J = JJ(H) = I, a matrix A is an element of C-nxn is termed generalized Hamiltonian matrix if JAJ = A(H). In this paper, an iterative method is constructed to solve the generalized Hamiltonian solutions of the coupled Sylvester matrix equations with conjugate transpose. It is proved that the iterative method is unconditionally convergent for any initial generalized Hamiltonian matrices. With it, the generalized Hamiltonian solutions can be obtained within finite iteration steps in the absence of roundoff errors. Finally, numerical examples are presented to illustrate the efficiency and applicability of the method.