Perturbation theory for Hermitian quadratic eigenvalue problem – damped and simultaneously diagonalizable systems

摘要: Abstract The main contribution of this paper is a novel approach to the perturbation theory structured Hermitian quadratic eigenvalue problems ( λ 2 M + D K ) x = 0 . We propose new concept without linearization, considering two structures: general (QEP) and simultaneously diagonalizable (SDQEP). Our first results are upper bounds for difference | ∥ X * ˜ 1 F − , where columns [ … k ] n linearly independent right eigenvectors positive definite matrix. As an application these we present bound SDQEP. third result lower sin Θ matrix canonical angles between eigensubspaces spanned by set SDQEP corresponding perturbed eigenvectors. quality mentioned have been illustrated numerical examples.