Integration on a convex polytope

Lasserre, Jean

doi:10.1090/S0002-9939-98-04454-2

Integration on a convex polytope
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by Jean B. Lasserre

Proc. Amer. Math. Soc. 126 (1998), 2433-2441

DOI: https://doi.org/10.1090/S0002-9939-98-04454-2

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Abstract:

We present an exact formula for integrating a (positively) homogeneous function $f$ on a convex polytope $\Omega \subset R^n$. We show that it suffices to integrate the function on the $(n-1)$-dimensional faces of $\Omega$, thus reducing the computational burden. Further properties are derived when $f$ has continuous higher order derivatives. This result can be used to integrate a continuous function after approximation via a polynomial.

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