Solving pencil problem generalized using Cholesky like-decomposition for skew-Hamiltonian matrix

We present in this paper a new method for solving skew-Hamiltonian/Hamiltonian generalized eigenvalue problem. The theoretical and practical aspects are treated. The skew-Hamiltonian/Hamiltonian pencil is converted to a standard Hamiltonian eigenproblem using Cholesky like-decomposition for skew-Hamiltonian matrix. This approach is more efficient as there is no need of calculation the reverse of a skew-Hamiltonian matrix. Numerical examples are given to show the effectiveness of the proposed method.