A NUMERICALLY STABLE, STRUCTURE PRESERVING METHOD FOR COMPUTING THE EIGENVALUES OF REAL HAMILTONIAN OR SYMPLECTIC PENCILS

A new method is presented for the numerical computation of the general ized eigenvalues of real Hamiltonian or symplectic pencils and matrice s. The method is numerically backward stable and preserves the structu re (i.e., Hamiltonian or symplectic). In the case of a Hamiltonian mat rix the method is closely related to the square reduced method of Van Loan, but in contrast to that method which may suffer from a loss of a ccuracy of order root epsilon, where epsilon is the machine precision, the new method computes the eigenvalues to full possible accuracy.