Integration on a convex polytope

被引：57

作者：

Lasserre, JB ^{[1
]}

机构：

[1] CNRS, LAAS, F-31077 Toulouse 4, France

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1998年 / 126卷 / 08期

关键词：

numerical integration in R-n; homogeneous functions; convex polytopes;

D O I：

10.1090/S0002-9939-98-04454-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present an exact formula for integrating a (positively) homogeneous function f on a convex polytope Omega subset of 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.

引用

页码：2433 / 2441

页数：9

共 6 条

[1] COMPUTING THE VOLUME, COUNTING INTEGRAL POINTS, AND EXPONENTIAL-SUMS [J].