Relative perturbation theory for quadratic Hermitian eigenvalue problems

Abstract

In this paper, we derive new relative perturbation bounds for eigenvectors and eigenvalues for regular quadratic eigenvalue problems of the form (λ2M+λC+K)x=0, where M and K are nonsingular Hermitian matrices and C is a general Hermitian matrix. These results are based on new relative perturbation bounds for an equivalent regular Hermitian matrix pair A−λB. The new bounds can be applied to quadratic eigenvalue problems appearing in many relevant applications, such as mechanical models with indefinite damping. The quality of our bounds is demonstrated by several numerical experiments.