Naslov
Relative Perturbation Theory for Quadratic Hermitian Eigenvalue Problem

Autori
Benner, Peter ; Liang, Xin ; Miodragović, Suzana ; Truhar, Ninoslav

Izvornik
Linear algebra and its applications (0024-3795) 612 (2021); LAA-D-18-00776R2, 38

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Relative perturbation theory, quadratic eigenvalue problem, Hermitian quadratic matrix polynomial, Hermitian matrix pair

Sažetak
In this paper, we derive new relative perturbation bounds for eigenvectors and eigenvalues for regular quadratic eigenvalue problems of the form $(\lambda^2 M + \lambda C + K)x = 0$, 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 $A- \lambda B$. 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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