Hamiltonian Eigenvalue Symmetry for Quadratic Operator Eigenvalue Problems

Abstract

SFB393/04-09 October 2004 Abstract When the eigenvalues of a given eigenvalue problems are symmetric with respect to the real and the imaginary axes, we speak about a Hamiltonian eigenvalue symmetry or a Hamiltonian structure of the spectrum. This property can be exploited for an efficient computation of the eigenvalues. For some elliptic boundary value problems it is known that the derived eigenvalue problems have this Hamiltonian symmetry. Without having a specific application in mind, we trace the question, under which assumptions the spectrum of a given quadratic eigenvalue problem possesses the Hamiltonian structure.