Structured conditioning of Hamiltonian eigenvalue problems
Provides a theoretical framework for understanding perturbation sensitivity in Hamiltonian eigenvalue problems, relevant to numerical analysis and applications in physics and engineering.
The paper characterizes the worst-case effect of structure-preserving perturbations on Hamiltonian eigenvalue problems, deriving expressions for structured condition numbers. It shows that for purely imaginary eigenvalues, standard unstructured perturbation analysis suffices.
We discuss the effect of structure-preserving perturbations on complex or real Hamiltonian eigenproblems and characterize the structured worst-case effect perturbations. We derive significant expressions for both the structured condition numbers and the worst-case effect Hamiltonian perturbations. It is shown that, for purely imaginary eigenvalues, the usual unstructured perturbation analysis is sufficient.