The Impact of the Properties of the Stiffness Matrix on Definite Quadratic Eigenvalue Problems - Kostić, Aleksandra; Voss, Heinrich; Timotić, Valentina (Sarajevo Journal of Mathematics, 2024)
Waiving the positive definiteness of the leading matrix A in a hyperbolic quadratic eigenvalue problem Q(λ)x=(λ^2A+λ B+C)x=0, x eq 0 one obtains a definite eigenvalue problem, which is known to have 2n eigenvalues in R{∞}. One of the characterizations of the definite quadratic eigenvalue problem is the existence of parameters ξ and μ so that Q(μ) is positive definite and Q(ξ) is negative definite, where ξ and μ are not known in advance. In this paper we consider the impact of the properties of the stiffness matrix C of the quadratic pencil Q(λ) on the corresponding definite quadratic eigenvalue problem and on the localization of the parameters ξ and μ.