Volume Of Sub-level Sets Of Homogeneous Polynomials

24 Oct 2018 · Lasserre Jean LAAS-MAC ·

Consider the sub level set K := {x : g(x) $\le$ 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.