Perturbation of purely imaginary eigenvalues of Hamiltonian matrices under structured perturbations

Abstract

The perturbation theory for purely imaginary eigenvaluesof Hamiltonian matrices under Hamiltonian and non-Hamiltonian perturbations is discussed. It is shown that there is a substantial difference in the behavior under these perturbations. The perturbation of real eigenvalues of real skew-Hamiltonian matrices under structured perturbations is discussed as well and these results are used to analyze the properties of the URV method for computing the eigenvalues of Hamiltonian matrices.