Generalized conjugate direction method for solving a class of generalized coupled Sylvester-conjugate transpose matrix equations over generalized Hamiltonian matrices

In this paper, a generalized conjugate direction (GCD) method for finding the generalized Hamiltonian solutions of a class of generalized coupled Sylvester-conjugate transpose matrix equations is proposed. Furthermore, it is proved that the algorithm can compute the least Frobenius norm generalized Hamiltonian solution group of the problem by choosing a special initial matrix group within a finite number of iterations in the absence of round-off errors. Numerical examples are also presented to illustrate the efficiency of the algorithm.