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Integration on a convex polytope

Author: Jean B. Lasserre
Journal: Proc. Amer. Math. Soc. 126 (1998), 2433-2441
MSC (1991): Primary 65D30
MathSciNet review: 1459132
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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.

References [Enhancements On Off] (What's this?)

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Additional Information

Jean B. Lasserre
Affiliation: LAAS-CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cédex 4, France

Keywords: Numerical integration in $R^n$, homogeneous functions, convex polytopes
Received by editor(s): August 5, 1996
Received by editor(s) in revised form: January 6, 1997
Communicated by: David Sharp
Article copyright: © Copyright 1998 American Mathematical Society

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