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Approximate Volume and Integration for Basic Semialgebraic Sets
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DOI：10.1137/080730287.png)
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Abstract
En 中文
Given a basic compact semialgebraic set K subset of R(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, which permits the approximation of the integral on K of any given polynomial; the 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
volume
integration
K-moment problem
semidefinite programming
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