Eigenvalue perturbation theory gives O(ε²) and O(ε³) accurate approximations of the pseudospectral abscissa, and fixed-point iterations initialized by these approximations find the global rightmost pseudospectral point in most tested cases.
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Approximation of the Pseudospectral Abscissa via Eigenvalue Perturbation Theory
Eigenvalue perturbation theory gives O(ε²) and O(ε³) accurate approximations of the pseudospectral abscissa, and fixed-point iterations initialized by these approximations find the global rightmost pseudospectral point in most tested cases.