2022 - Francophone Computer Algebra Days - Journées nationales de calcul formel

Collection 2022 - Francophone Computer Algebra Days - Journées nationales de calcul formel

Organizer(s) Paola Boito (University of Pisa) Eleonora Guerrini (Université de Montpellier) Pierre-Vincent Koseleff (Institut de Mathématiques de Jussieu – Paris Rive Gauche) Pierre-Jean Spaenlehauer (INRIA Nancy Grand-Est) Tristan Vaccon (Université de Limoges)

Date(s) 28/02/2022 - 04/03/2022

linked URL https://conferences.cirm-math.fr/2568.html

00:00:00 / 00:00:00

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

By Mioara Joldes

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).

Information about the video

Date of recording 03/03/2022
Date of publication 17/03/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19893803
Cite this video Joldes, Mioara (03/03/2022). Validated symbolic-numeric algorithms and practical applications in aerospace - Lecture 2. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19893803
URL https://dx.doi.org/10.24350/CIRM.V.19893803

Domain(s)

Bibliography

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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