Volume of sub-level sets of polynomials
Résumé
Consider the sub-level set K := {x : g(x) ≤ 1} of a nonnegative homogeneous polynomial g. We show that its Lebesgue volume vol(K) can be approximated as closely as desired by solving a sequence of generalized eigenvalue problems with respect to a pair of Hankel matrices of increasing size, whose entries are obtained in closed form. An extension to the non-homogeneous case is also briefly described.
Domaines
Optimisation et contrôle [math.OC]| Origine | Fichiers produits par l'(les) auteur(s) |
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