Set-Membership Computation of Integrals with Uncertain Endpoints

Olivier Mullier; Julien Alexandre dit Sandretto

doi:10.1007/978-3-030-40616-5_13

Set-Membership Computation of Integrals with Uncertain Endpoints

Olivier Mullier
, Julien Alexandre dit Sandretto

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

Résumé

An efficient guaranteed method for the computation of the integral of a nonlinear continuous function between two interval endpoints is proposed. This computation can be of interest for the computation of global optimization problems where such integrals occur like in robotics. The method results in the computation of the minimum and maximum of these integrals and provides the endpoints at stake. The complexity of the resulting algorithms is discussed, it depends on the number of roots of the function to be integrated. The computation is illustrated on several examples.

langue originale	Anglais
titre	Numerical Computations
Sous-titre	Theory and Algorithms - 3rd International Conference, NUMTA 2019, Revised Selected Papers
rédacteurs en chef	Yaroslav D. Sergeyev, Dmitri E. Kvasov, Yaroslav D. Sergeyev, Dmitri E. Kvasov
Editeur	Springer
Pages	169-181
Nombre de pages	13
ISBN (imprimé)	9783030406158
Les DOIs	https://doi.org/10.1007/978-3-030-40616-5_13
état	Publié - 1 janv. 2020
Evénement	3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019 - Crotone, Italie Durée: 15 juin 2019 → 21 juin 2019

Série de publications

Nom	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11974 LNCS
ISSN (imprimé)	0302-9743
ISSN (Electronique)	1611-3349

Une conférence

Une conférence	3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019
Pays/Territoire	Italie
La ville	Crotone
période	15/06/19 → 21/06/19

Accès au document

10.1007/978-3-030-40616-5_13

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Mullier, O., & Alexandre dit Sandretto, J. (2020). Set-Membership Computation of Integrals with Uncertain Endpoints. Dans Y. D. Sergeyev, D. E. Kvasov, Y. D. Sergeyev, & D. E. Kvasov (eds.), Numerical Computations: Theory and Algorithms - 3rd International Conference, NUMTA 2019, Revised Selected Papers (p. 169-181). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol 11974 LNCS). Springer. https://doi.org/10.1007/978-3-030-40616-5_13

Mullier, Olivier ; Alexandre dit Sandretto, Julien. / Set-Membership Computation of Integrals with Uncertain Endpoints. Numerical Computations: Theory and Algorithms - 3rd International Conference, NUMTA 2019, Revised Selected Papers. Editeur / Yaroslav D. Sergeyev ; Dmitri E. Kvasov ; Yaroslav D. Sergeyev ; Dmitri E. Kvasov. Springer, 2020. p. 169-181 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "An efficient guaranteed method for the computation of the integral of a nonlinear continuous function between two interval endpoints is proposed. This computation can be of interest for the computation of global optimization problems where such integrals occur like in robotics. The method results in the computation of the minimum and maximum of these integrals and provides the endpoints at stake. The complexity of the resulting algorithms is discussed, it depends on the number of roots of the function to be integrated. The computation is illustrated on several examples.",

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Mullier, O & Alexandre dit Sandretto, J 2020, Set-Membership Computation of Integrals with Uncertain Endpoints. Dans YD Sergeyev, DE Kvasov, YD Sergeyev & DE Kvasov (eds), Numerical Computations: Theory and Algorithms - 3rd International Conference, NUMTA 2019, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), VOL. 11974 LNCS, Springer, p. 169-181, 3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019, Crotone, Italie, 15/06/19. https://doi.org/10.1007/978-3-030-40616-5_13

Set-Membership Computation of Integrals with Uncertain Endpoints. / Mullier, Olivier; Alexandre dit Sandretto, Julien.
Numerical Computations: Theory and Algorithms - 3rd International Conference, NUMTA 2019, Revised Selected Papers. Ed. / Yaroslav D. Sergeyev; Dmitri E. Kvasov; Yaroslav D. Sergeyev; Dmitri E. Kvasov. Springer, 2020. p. 169-181 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol 11974 LNCS).

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

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AU - Mullier, Olivier

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N2 - An efficient guaranteed method for the computation of the integral of a nonlinear continuous function between two interval endpoints is proposed. This computation can be of interest for the computation of global optimization problems where such integrals occur like in robotics. The method results in the computation of the minimum and maximum of these integrals and provides the endpoints at stake. The complexity of the resulting algorithms is discussed, it depends on the number of roots of the function to be integrated. The computation is illustrated on several examples.

AB - An efficient guaranteed method for the computation of the integral of a nonlinear continuous function between two interval endpoints is proposed. This computation can be of interest for the computation of global optimization problems where such integrals occur like in robotics. The method results in the computation of the minimum and maximum of these integrals and provides the endpoints at stake. The complexity of the resulting algorithms is discussed, it depends on the number of roots of the function to be integrated. The computation is illustrated on several examples.

KW - Integral

KW - Interval methods

KW - Set-membership computation

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DO - 10.1007/978-3-030-40616-5_13

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Numerical Computations

A2 - Sergeyev, Yaroslav D.

A2 - Kvasov, Dmitri E.

A2 - Sergeyev, Yaroslav D.

A2 - Kvasov, Dmitri E.

PB - Springer

T2 - 3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019

Y2 - 15 June 2019 through 21 June 2019

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Mullier O, Alexandre dit Sandretto J. Set-Membership Computation of Integrals with Uncertain Endpoints. Dans Sergeyev YD, Kvasov DE, Sergeyev YD, Kvasov DE, rédacteurs en chef, Numerical Computations: Theory and Algorithms - 3rd International Conference, NUMTA 2019, Revised Selected Papers. Springer. 2020. p. 169-181. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-40616-5_13

Set-Membership Computation of Integrals with Uncertain Endpoints

Résumé

Série de publications

Une conférence

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Autres fichiers et liens

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