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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	Numerical Computations
Subtitle of host publication	Theory and Algorithms - 3rd International Conference, NUMTA 2019, Revised Selected Papers
Editors	Yaroslav D. Sergeyev, Dmitri E. Kvasov, Yaroslav D. Sergeyev, Dmitri E. Kvasov
Publisher	Springer
Pages	169-181
Number of pages	13
ISBN (Print)	9783030406158
DOIs	https://doi.org/10.1007/978-3-030-40616-5_13
Publication status	Published - 1 Jan 2020
Event	3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019 - Crotone, Italy Duration: 15 Jun 2019 → 21 Jun 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11974 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019
Country/Territory	Italy
City	Crotone
Period	15/06/19 → 21/06/19

Keywords

Integral
Interval methods
Set-membership computation

Access to Document

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

Cite this

Mullier, O., & Alexandre dit Sandretto, J. (2020). Set-Membership Computation of Integrals with Uncertain Endpoints. In 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 (pp. 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. editor / Yaroslav D. Sergeyev ; Dmitri E. Kvasov ; Yaroslav D. Sergeyev ; Dmitri E. Kvasov. Springer, 2020. pp. 169-181 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Set-Membership Computation of Integrals with Uncertain Endpoints",

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.",

keywords = "Integral, Interval methods, Set-membership computation",

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doi = "10.1007/978-3-030-40616-5\_13",

language = "English",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer",

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Mullier, O & Alexandre dit Sandretto, J 2020, Set-Membership Computation of Integrals with Uncertain Endpoints. in 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, pp. 169-181, 3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019, Crotone, Italy, 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).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Alexandre dit Sandretto, Julien

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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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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. In Sergeyev YD, Kvasov DE, Sergeyev YD, Kvasov DE, editors, 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

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