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Set-Membership Computation of Integrals with Uncertain Endpoints

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Numerical Computations: Theory and Algorithms (NUMTA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11974))

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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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Acknowledgement

This research was supported by the “Complex Systems Engineering Chair - Ecole Polytechnique, THALES, DGA, FX, DASSAULT AVIATION, DCNS Research, ENSTA ParisTech, Télécom ParisTech, Fondation ParisTech and FDO ENSTA”. This research is also partially funded by DGA MRIS.

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Authors and Affiliations

  1. ENSTA Paris, 828 bd des maréchaux, 91120, Palaiseau, France

    Olivier Mullier & Julien Alexandre dit Sandretto

Authors
  1. Olivier Mullier
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  2. Julien Alexandre dit Sandretto
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Correspondence to Olivier Mullier .

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Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

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Mullier, O., Alexandre dit Sandretto, J. (2020). Set-Membership Computation of Integrals with Uncertain Endpoints. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11974. Springer, Cham. https://doi.org/10.1007/978-3-030-40616-5_13

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  • DOI: https://doi.org/10.1007/978-3-030-40616-5_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-40615-8

  • Online ISBN: 978-3-030-40616-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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