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VOLUME OF SUBLEVEL SETS OF HOMOGENEOUS POLYNOMIALS

Jean Lasserre 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : Consider the sub level set K := {x : g(x) ≤ 1} where g is a positive and homogeneous polynomial. We show that its Lebesgue volume 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, and whose entries are obtained in closed form.
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Contributor : Jean Bernard Lasserre <>
Submitted on : Sunday, April 14, 2019 - 5:09:33 PM
Last modification on : Thursday, June 10, 2021 - 3:07:10 AM

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Jean Lasserre. VOLUME OF SUBLEVEL SETS OF HOMOGENEOUS POLYNOMIALS. SIAM Journal on Applied Algebra and Geometry, Society for Industrial and Applied Mathematics 2019, 3 (2), pp.372-389. ⟨10.1137/18M1222478⟩. ⟨hal-01898429v4⟩

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