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Taylor Series Revisited

Thirioux, Xavier and Maffart, Alexis Taylor Series Revisited. (2019) In: International Colloquium on Theoretical Aspects of Computing (ICTAC 2019), 31 October 2019 - 4 November 2019 (Hammamet, Tunisia).

(Document in English)

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Official URL: https://doi.org/10.1007/978-3-030-32505-3_19


We propose a renovated approach around the use of Taylor expansions to provide polynomial approximations. We introduce a coinductive type scheme and finely-tuned operations that altogether constitute an algebra, where our multivariate Taylor expansions are first-class objects. As for applications, beyond providing classical expansions of integro-differential and algebraic expressions mixed with elementary functions, we demonstrate that solving ODE and PDE in a direct way, without external solvers, is also possible. We also discuss the possibility of computing certified errors within our scheme.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to Springer editor. This papers appears in volume 11884 of Lecture Notes in Computer Science ISSN: 0302-9743 ISBN 978-3-030-32504-6 The original PDF is available at: https://link.springer.com/chapter/10.1007%2F978-3-030-32505-3_19
HAL Id:hal-02950743
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Laboratory name:
Deposited On:14 Sep 2020 14:22

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