A new method for the Hamiltonian eigenvalue problem

A new method is presented for the numerical computation of the eigenvalues of real Hamiltonian matrices. The method is strongly backward stable, i.e. it is numerically backward stable and preserves the Hamiltonian structure. It is closely related to the square reduced method of Van Loan, but in contrast to that method which may suffer from a loss of accuracy of order √ε. where ε is the machine precision, the new method computes the eigenvalues to full possible accuracy.