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Volume of sub-level sets of 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} 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.
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https://hal.laas.fr/hal-02277745
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Submitted on : Tuesday, September 3, 2019 - 9:32:05 PM
Last modification on : Thursday, June 10, 2021 - 3:03:12 AM
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Jean Lasserre. Volume of sub-level sets of polynomials. 18th European Control Conference (ECC 2019), Jun 2019, Naples, Italy. pp.1975-1980, ⟨10.23919/ECC.2019.8795995⟩. ⟨hal-02277745⟩

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