Relative perturbation theory for quadratic Hermitian eigenvalue problems

In this paper, we derive new relative perturbation bounds for eigenvectors and eigenvalues regular quadratic eigenvalue problems of the form $\lambda^2 M x + \lambda C K = 0$, where $M$ $K$ are nonsingular Hermitian matrices $C$ is a general matrix. We base our findings on results an equivalent matrix pair $A-\lambda B$. The can be applied to many interesting appearing in applications, such as mechanical models with indefinite damping. quality demonstrated by several numerical experiments.