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

• First-order factors of linear Mahler operators. With Frédéric Chyzak, Thomas Dreyfus, and Philippe Dumas. 2024. [arXiv]
• Rounding Error Analysis of an Orbital Collision Probability Evaluation Algorithm. With Denis Arzelier, Florent Bréhard, and Mioara Joldes. ARITH 2024. [HAL]
• Computing error bounds for asymptotic expansions of regular P-recursive sequences. With Ruiwen Dong and Stephen Melczer. Mathematics of Computation 93:977–1017, 2024, doi:10.1090/mcom/3888. [arXiv]
• 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]
• 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]
• 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]
• 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]
• 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]
• Truncation Bounds for Differentially Finite Series. Annales Henri Lebesgue 2:99–148, 2019, doi:10.5802/ahl.17. [bib] [pdf] [HAL]
• 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]
• 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]
• 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]
• Rigorous Uniform Approximation of D-Finite Functions Using Chebyshev Expansions. With Alexandre Benoit and Mioara Joldes. 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]
• 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”)

• 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]
• 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]
• 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

• 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

• ore_algebra-analytic: symbolic-numeric features for ore_algebra. Mostly supersedes NumGfun. [github] [doc] [www] [online demo (binder)]
• SageMath contributions: commits, issues
• PythonSollya: Cython bindings for the Sollya library, developed with Nicolas Brunie. [gitlab]
• NumGfun: a Maple module for manipulating D-finite analytic functions. NumGfun is no longer actively developed (though still maintained), and superseded for most purposes by a newer SageMath implementation. Please consider trying the new code! Distributed as a submodule of gfun, under the GNU LGPL v. 2.1. [www] [gitlab] [doc]
• mmaple: a half-finished Mathemagix module to interface Mathemagix with Maple. [svn]
• Miscellaneous research-related code

Recent & Selected Talks

• On the practical computation of Stokes matrices. Journées NuSCAP, Paris, May 22, 2024. [slides]
• 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

• Some internship offers (in French):
  • Code generation for the evaluation of Bessel functions,
  • intership proposals in the framework of the NODE project.
  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.

Contact Information

• Email: marc (A) mezzarobba DOT net (firstname at lastname dot net).
• PGP key:

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      Key fingerprint = C6D1 A8CD 1101 4E72 9BBB  3FCA 9B73 BD05 52CC B003
  sub   4096R/0xECED4C2F991E2B2C 2015-04-25
  sub   4096R/0xEA12302691E81A33 2015-04-25

• vCard
• Work:
  Marc Mezzarobba
  LIX
  1 rue Honoré d'Estienne d'Orves
  Bâtiment Alan Turing
  CS35003
  91120 Palaiseau
  
  ☎ +33 1 77 57 03 07
• Home: [map]
  
  Marc Mezzarobba
  40, rue des Ruelles
  F-91300 Massy
  
  ☎ +33 9 50 09 81 95