Relative Perturbation Theory for Quadratic Eigenvalue Problems
Peter Benner, Xin Liang, Suzana Miodragović, Ninoslav Truhar · Max Planck Digital Library · 2016
In this paper, we derive new relative perturbation bounds for eigenvectors and eigenvalues for regular quadratic eigenvalue problems of the form λ 2 M x + λCx + Kx = 0, where M and K are nonsingular Hermitian matrices and C is a general Hermitian matrix.We base our findings on new results for an equivalent regular Hermitian matrix pair A -λB.The new bounds can be applied to many interesting quadratic eigenvalue problems appearing in applications, such as mechanical models with indefinite damping.The quality of our bounds is demonstrated by several numerical experiments.