Minimum-norm Hamiltonian solutions of a class of generalized Sylvester-conjugate matrix equations

In this study, we consider the iteration solutions of the generalized Sylvester-conjugate matrix equation: AXB+CX¯D=E by a modified conjugate gradient method. When the system is consistent, the convergence theorem shows that a solution can be obtained within finite iterative steps in the absence of round-off error for any initial value given Hamiltonian matrix. Furthermore, we can get the minimum-norm solution X∗ by choosing a special kind of initial matrix. Finally, some numerical examples are given to demonstrate the algorithm considered is quite effective in actual computation.