Marc Mezzarobba
Chargé de recherche au
CNRS,
LIX,
équipe MAX
Alan Turing building, room 1012
[postal address]
[map]
[access]
✍ marc (A) mezzarobba DOT net
☎ +33 1 82 72 03 07
pgp 0x9b73bd0552ccb003
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Publications
Software
Talks
Internships
Contact
(Pre-)Publications
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Computing error bounds for asymptotic expansions of regular P-recursive sequences.
With
Ruiwen Dong and
Stephen Melczer,
2023.
To appear in Mathematics of Computation,
doi:10.1090/mcom/3888.
[arXiv]
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Symbolic-Numeric Factorization of Differential Operators.
With
Frédéric Chyzak and
Alexandre Goyer.
ISSAC 2022,
doi:10.1145/3476446.3535503.
[pdf]
[HAL]
-
Fast evaluation of some p-adic transcendental functions.
With
Xavier Caruso,
Nobuki Takayama, and
Tristan Vaccon.
Working draft, 2021.
[HAL]
-
Sequence Positivity Through Numeric Analytic Continuation: Uniqueness of the Canham Model for Biomembranes.
With
Stephen Melczer.
Combinatorial Theory 2(2), 2022,
doi:10.5070/C62257847.
[HAL]
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Rounding Error Analysis of Linear Recurrences Using Generating Series.
Electronic Transactions on Numerical Analysis 58:196–227, 2023,
doi:10.1553/etna_vol58s196.
[pdf]
[supplements]
[HAL]
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The expected signature of Brownian motion stopped on the boundary of a circle has finite radius of convergence.
With
Horatio Boedihardjo,
Joscha Diehl, and
Hao Ni.
Bulletin of the London Mathematical Society 53(1):285–299, 2021,
doi:10.1112/blms.12420.
[pdf]
[arXiv]
[HAL]
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Multivariate Ore Polynomials in SageMath.
With
Manuel Kauers.
ISSAC 2019 software presentation abstract.
ACM Communications in Computer Algebra 53(2):57–60, 2019,
doi:10.1145/3371991.3371998.
[bib]
[pdf]
[HAL]
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Computing the volume of compact semi-algebraic sets.
With
Pierre Lairez and
Mohab Safey El Din.
ISSAC 2019,
pages 259–266,
doi:10.1145/3326229.3326262.
[bib]
[pdf]
[HAL]
[arXiv]
[code]
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Truncation Bounds for Differentially Finite Series.
Annales Henri Lebesgue 2:99–148, 2019,
doi:10.5802/ahl.17.
[bib]
[pdf]
[HAL]
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Fast and rigorous arbitrary-precision computation of Gauss-Legendre quadrature nodes and weights.
With
Fredrik Johansson.
SIAM Journal on Scientific Computing 40(6):C726–C747, 2018,
doi:10.1137/18M1170133.
[pdf]
[HAL]
[arXiv]
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Computing solutions of linear Mahler equations.
With
Frédéric Chyzak,
Thomas Dreyfus, and
Philippe Dumas.
Mathematics of Computation 87(314):2977–3021, 2018,
doi:10.1090/mcom/3359.
[bib]
[pdf]
[HAL]
[arXiv]
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Rigorous Multiple-Precision Evaluation of D-Finite Functions in SageMath.
2016.
Accepted for publication in the proceedings of
ICMS 2016,
but withdrawn due to a disagreement with Springer on copyright matters.
[bib]
[pdf]
[HAL]
[arXiv]
[talk]
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Rigorous Uniform Approximation of D-Finite Functions Using Chebyshev Expansions.
With
Alexandre Benoit and
Mioara Joldeș.
Mathematics of Computation 86(305):1303–1341, 2017,
doi:10.1090/mcom/3135.
Supersedes Chapter 9 of my thesis.
[bib]
[pdf]
[HAL]
[arXiv]
[code]
-
Comparison between binary and decimal floating-point numbers.
With
Nicolas Brisebarre,
Christoph Lauter, and
Jean-Michel Muller.
Extended version of our ARITH 2013 article.
IEEE Transactions on Computers,
65(7):2032–2044, 2016,
doi:10.1109/TC.2015.2479602.
[bib]
[pdf]
[HAL]
[code]
-
Semi-Automatic Floating-Point Implementation of Special Functions.
With
Christoph Lauter.
ARITH 22 (2015).
[bib]
[pdf]
[HAL]
[code]
-
Finding Hyperexponential Solutions of Linear ODEs by Numerical Evaluation.
With
Fredrik Johansson and
Manuel Kauers.
ISSAC 2013.
[bib]
[pdf]
[arXiv]
-
Multiple precision evaluation of the Airy Ai function with reduced cancellation.
With
Sylvain Chevillard.
ARITH 21 (2013).
[bib]
[pdf]
[HAL]
[arXiv]
[code]
[talk]
-
Comparison between binary64 and decimal64 floating-point numbers.
With
Nicolas Brisebarre,
Christoph Lauter, and
Jean-Michel Muller.
ARITH 21 (2013).
(Superseded by an extended version.)
[bib]
[pdf]
[HAL]
[code]
-
A Note on the Space Complexity of Fast D‑Finite Function Evaluation.
CASC 2012.
[bib]
[pdf]
[HAL]
[arXiv]
[talk]
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The Dynamic Dictionary of Mathematical Functions (DDMF).
With
Alexandre Benoit,
Frédéric Chyzak,
Alexis Darrasse,
Stefan Gerhold, and
Bruno Salvy.
ICMS 2010
(LNCS 6327), pages 35-41,
doi:10.1007/978-3-642-15582-6_7.
[bib]
[pdf]
[HAL]
-
NumGfun: a Package for Numerical and Analytic Computation with D-finite Functions.
ISSAC 2010,
pages 139-146,
doi:10.1145/1837934.1837965.
(Significantly extended French version in Chapters 1, 7, and 8 of my PhD thesis.)
[bib]
[pdf]
[HAL]
[arXiv]
[talk]
[code]
[manual]
-
Effective Bounds for P-Recursive Sequences.
With Bruno Salvy.
Journal of Symbolic Computation 45(10):1075–1096, 2010,
doi:10.1016/j.jsc.2010.06.024.
(Extended French version available in Chapters 4 and 5 of my thesis.)
[bib]
[pdf (preliminary version)]
[arXiv]
[code]
-
Computing roadmaps in smooth real algebraic sets.
With Mohab Safey El Din.
Transgressive Computing 2006.
[bib]
[pdf]
[HAL]
Calcul mathématique avec Sage (aka the “French Sage Book”)
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Computational Mathematics with SageMath.
(Updated English translation of Calcul mathématique avec Sage.)
Paul Zimmermann,
Alexandre Casamayou,
Nathann Cohen,
Guillaume Connan,
Thierry Dumont,
Laurent Fousse,
François Maltey,
Matthias Meulien,
Marc Mezzarobba,
Clément Pernet,
Nicolas M. Thiéry,
Erik Bray,
John Cremona,
Marcelo Forets,
Alexandru Ghitza,
Hugh Thomas.
SIAM, 2018.
ISBN 9781611975451.
[bib]
[www]
[buy from SIAM]
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Calcul mathématique avec Sage.
(Original French edition.)
With
Alexandre Casamayou,
Nathann Cohen,
Guillaume Connan,
Thierry Dumont,
Laurent Fousse,
François Maltey,
Matthias Meulien,
Clément Pernet,
Nicolas M. Thiéry, and
Paul Zimmermann
(coordinator).
CreateSpace, 2013.
ISBN 1481191047.
[bib]
[www]
[amazon.fr]
[HAL]
Dissertations and Reports (in French)
-
Autour de l'évaluation numérique des fonctions D-finies.
Thèse de doctorat (PhD thesis), École polytechnique, 2011.
[bib]
[pdf]
[TEL]
[code]
[defense]
-
Génération automatique de procédures numériques pour les fonctions D-finies.
Master thesis (supervised by Bruno Salvy),
Master parisien de recherche en informatique, 2007.
[bib]
[pdf]
[www]
[defense]
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Analyse en théorie et en pratique du calcul de cartes routières.
Research internship report (supervised by Mohab Safey El Din, LIP6), 2005.
Available upon request.
-
Comment démontrer des formules sans effort.
`Maîtrise' report, with
Sam Zoghaib,
supervised by
François Loeser,
2005.
[pdf]
Notes and Other Writings
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Précision arbitraire : complexité, séries.
Lecture notes.
2021.
[pdf]
-
Récurrences, méthode de Miller.
Lecture notes.
2016.
[pdf]
-
NumGfun User Manual.
Last updated September 3, 2014.
[pdf]
-
Polynomial Approximation and Floating-Point Numbers.
Summary of a talk by
Sylvain Chevillard,
proceedings of séminaire Algo,
2007.
[pdf]
-
Computing Monodromy Groups Defined by Plane Algebraic Curves.
Summary of a talk by
Adrien Poteaux,
2007.
[pdf]
Software
Recent & Selected Talks
- Error Analysis of Linear Recurrences using Generating Series.
Differential Seminar @ RTCA,
Paris,
November 30, 2023.
[slides]
- Asymptotic Expansions with Error Bounds for Solutions of Linear Recurrences.
AriC Seminar,
Lyon,
June 15, 2023.
[slides]
- Regular Singularities & Rigorous Numerics.
Periods workgroup, online,
May 19, 2021.
[slides]
[online demo]
- Analyse d'erreur de récurrences à l'aide de séries génératrices.
Séminaire AriC,
en ligne,
21 janvier 2021.
[slides]
- Interval Summation of Differentially Finite Series.
MAX Seminar,
online,
April 28, 2020.
[slides]
- Rigorous Numerics for Differentially Finite Functions.
Computing with D-Modules II,
Leipzig,
September 3, 2019.
[slides]
[ipynb]
[online demo]
- Recent improvements to ore_algebra.
FastRelax Final Workshop,
Lyon,
May 23, 2019.
[ipynb]
[nbviewer]
-
Truncation Bounds for Differentially Finite Series.
Journées FastRelax,
Sophia-Antipolis,
June 5, 2018.
[slides]
Research Internships & Projects for Students
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Some internship offers (in French):
Please contact me if you are interested!
These project topics are mainly intended for M2 level internships, but some could be adapted to other contexts.
-
Some student projets I had the pleasure of supervising.
