Perturbation of eigenvalues of matrix pencils and the optimal assignment problem
Marianne Akian, R.B. Bapat, Stéphane Gaubert · Comptes Rendus Mathématique · 2004
We extend the perturbation theory of Višik, Ljusternik and Lidskiı̆ to the case of eigenvalues of matrix pencils. This extension allows us to solve certain degenerate cases of this theory. We show that the first order asymptotics of the eigenvalues of a perturbed matrix pencil can be computed generically by methods of min-plus algebra and optimal assignment algorithms. We illustrate this result by discussing a singular perturbation problem considered by Najman.