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Validated symbolic-numeric algorithms and practical applications in aerospace - Lecture 2

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Auteurs : Joldes, Mioara (Auteur de la conférence)
CIRM (Editeur )

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Résumé : In various fields, ranging from aerospace engineering or robotics to computer-assisted mathematical proofs, fast and precise computations are essential. Validated (sometimes called rigorous as well) computing is a relatively recent field, developed in the last 20 years, which uses numerical computations, yet is able to provide rigorous mathematical statements about the obtained result, such as guaranteed and reasonably tight error bounds. This area of research deals with problems that cannot or are difficult and costly in time to be solved by traditional mathematical methods, like problems that have a large search space, problems for which closed forms given by symbolic computations are not available or too difficult to obtain, or problems in nonlinear analysis.
In this course, we provide an introduction to several computing methods and algorithms developed based on the theory of set-valued analysis (in specific function spaces) as well as by combining symbolic and numerical computations. These techniques are illustrated with some applications related to the efficient finite precision evaluation of numerical functions (some of which appear in practical space mission analysis and design).

Mots-Clés : computer algebra; validated computing

Codes MSC :

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de Publication : 17/03/2022
    Date de Captation : 03/03/2022
    Sous Collection : Research School
    Catégorie arXiv : Symbolic Computation ; Numerical Analysis
    Domaine(s) : Algèbre ; Analyse Numérique & Calcul Formel ; Informatique ; Probabilités & Statistiques
    Format : MP4 (.mp4) - HD
    Durée : 01:22:04
    Audience : Chercheurs ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2022-03-03_Joldes_Part2.mp4

Informations sur la Rencontre

Nom de la Rencontre : Francophone Computer Algebra Days / JNCF - Journées nationales de calcul formel
Organisateurs de la Rencontre : Boito, Paola ; Guerrini, Eleonora ; Koseleff, Pierre-Vincent ; Spaenlehauer, Pierre-Jean ; Vaccon, Tristan
Dates : 28/02/2022 - 04/03/2022
Année de la rencontre : 2022
URL de la Rencontre : https://conferences.cirm-math.fr/2568.html

Données de citation

DOI : 10.24350/CIRM.V.19893803
Citer cette vidéo: Joldes, Mioara (2022). Validated symbolic-numeric algorithms and practical applications in aerospace - Lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19893803
URI : http://dx.doi.org/10.24350/CIRM.V.19893803

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Bibliographie

  • Tucker, Warwick. Validated Numerics: A Short Introduction to Rigorous Computations, Princeton: Princeton University Press, 2011. - https://doi.org/10.1515/9781400838974

  • F. Bréhard, N. Brisebarre, and M. Joldeş, “Validated and numerically efficient Chebyshev spectral methods for linear ordinary differential equations,” ACM Transactions on Mathematical Software (TOMS), vol. 44, no. 4, p. 44, 2018. - https://hal.archives-_ouvertes.fr/hal-_01526272/

  • R. Serra, D. Arzelier, M. Joldes, J.-B. Lasserre, A. Rondepierre, and B. Salvy, “Fast and accurate computation of orbital collision probability for short-term encounters,” Journal of Guidance, Control, and Dynamics, vol. 39, no. 5, pp. 1009–1021, 2016. - https://hal.archives-_ouvertes.fr/hal-_01132149/.



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