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## Principal Research Fellow

LAAS-CNRS, Toulouse, France

# Approximate volume and integration for basic semi-algebraic sets

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### Description

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**Title**: Approximate volume and integration for basic semi-algebraic sets

**Author(s)**: Didier Henrion, Jean Bernard Lasserre, Carlo Savorgnan

**Abstract**: Given a basic compact semi-algebraic set KsubsetR n, we introduce a methodology that generates a sequence converging to the volume of K. This sequence is obtained from optimal values of a hierarchy of either semidefinite or linear programs. Not only the volume but also every finite vector of moments of the probability measure that is uniformly distributed on K can be approximated as closely as desired, and so permits to approximate the integral on K of any given polynomial; extension to integration against some weight functions is also provided. Finally, some numerical issues associated with the algorithms involved are briefly discussed.

**Keywords**: computational geometry, integration, k moment problem, semidefinite, volume

**Subject**: unspecified

**Area**: Other

**Language**: English

**Year**: 2008

Affiliations : |
LAAS-CNRS, Toulouse, France |

**Journal**: Convergence

**Pages**: 1-22

**Url**: http://arxiv.org/abs/0807.2505

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- FJean Lasserre,
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- Jean Lasserre,
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