Approximate Volume and Integration for Basic Semialgebraic Sets

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F09%3A00158849" target="_blank" >RIV/68407700:21230/09:00158849 - isvavai.cz</a>

Result on the web

—

DOI - Digital Object Identifier

—

Result language

angličtina

Original language name

Approximate Volume and Integration for Basic Semialgebraic Sets

Original language description

Given a basic compact semialgebraic set K Rn, 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 volumebut 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.

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

—

Project

<a href="/en/project/GA102%2F08%2F0186" target="_blank" >GA102/08/0186: Algorithms for Complex Systems Analysis and Control Design</a><br>

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2009

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

SIAM REVIEW

ISSN

0036-1445

e-ISSN

—

Volume of the periodical

51

Issue of the periodical within the volume

4

Country of publishing house

US - UNITED STATES

Number of pages

22

Pages from-to

—

UT code for WoS article

000271983500005

EID of the result in the Scopus database

—