Integration on a convex polytope

Abstract

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