Clément Pernet Professeur Grenoble INP - UGA clement.pernet@univ-grenoble-alpes.fr

Grenoble INP - UGA, LJK - CAS3C3, Grenoble INP - UGA Laboratoire Jean Kuntzmann 700, avenue Centrale, Bâtiment IMAG CS 40700 38058 GRENOBLE Cedex 09 - France Office: 108 tel: +33 (0)4 57 42 17 97

Publications

My list of publications

• on hal
• on dblp
• on scholar
• on orcid

In the pipeline

• A non-commutative algorithm for multiplying 4x4 matrices using 48 non-complex multiplications( hal-05112145)
  J-G. Dumas, C. Pernet, A. Sedoglavic
  
• A non-commutative algorithm for multiplying 3x4 matrix by a 4x7 matrix using 63 non-complex multiplications( hal-05121550)
  J-G. Dumas, C. Pernet, A. Sedoglavic
  
• Towards automated generation of fast and accurate algorithms for recursive matrix multiplication (hal-04995684)
  J-G. Dumas, C. Pernet, A. Sedoglavic

Book chapters

• Computational Mathematics with SageMath, Ch. 8: Linear Algebra
  (online version, SIAM book)
  P. Zimmerman, A. Casamayou, N. Cohen, G. Connan, T. Dumont, L. Fousse, F. Maltey, M. Meulien, M. Mezzarobba, C. Pernet, N. Thiéry, E. Bray, J. Cremona, M. Forets ,A. Ghitza, H. Thomas
  SIAM, Distributed under license CC-by-sa. 464 pages. Dec. 2018
• Calcul mathématique avec Sage, Ch. 8: Algèbre linéaire
  (version électronique, impression sur Amazon.fr, Createspace)
  A. Casamayou, G. Connan, T. Dumont, L. Fousse, F. Maltey, M. Meulien, M. Mezzarobba, C. Pernet, N. Thiéry, P. Zimmermann
  Distribué sous license CC-by-sa
• Handbook of Finite Fields, Ch. Computational linear algebra over finite fields (CRC Press)
  G. Mullen and D Panario editors.

Articles in journals and refereed conference proceedings

2025

• Towards automated generation of fast and accurate algorithms for recursive matrix multiplication (hal-04995684, doi:10.1016/j.jsc.2025.102524)
  J-G. Dumas, C. Pernet, A. Sedoglavic
  J. of Symbolic Computation (134), May--June 2026

2024

• Strassen's algorithm is not optimally accurate( doi:10.1145/3666000.3669697, hal-04441653, Slides)
  J-G. Dumas, C. Pernet, A. Sedoglavic
  ISSAC'24
• Computing Krylov iterates in the time of matrix multiplication (doi:10.1145/3666000.3669715, hal-04445355, Slides)
  V. Neiger, C. Pernet, G. Villard
  ISSAC'24 (Distinguished paper award)
• High-order lifting for polynomial Sylvester matrices (doi:10.1016/j.jco.2023.101803, hal:03740320)
  C. Pernet, H. Signargout, G. Villard
  J. of Complexity (80) Feb. 2024

2023

• Exact Computations with quasiseparable matrices (doi:10.1145/3597066.3597102, hal-03978799)
  C. Pernet, H. Signargout, G. Villard
  ISSAC'23
• VESPo: Verified Evaluation of Secret Polynomials: with application to low-storage dynamic proofs of retrievability (hal:03365854)
  J-G. Dumas, A. Maignan, C. Pernet, D. Roche
  PoPETS'23
• Some fast algorithms multiplying a matrix by its adjoint (doi:10.1016/j.jsc.2022.08.009, hal:03095393)
  J-G. Dumas, C. Pernet, A. Sedoglavic
  J. of Symbolic Computation, Special Issue on ISSAC'20. (115) 2023

2021

• Dynamic proofs of retrievability with low server storage (@USENIX, hal:02875379)
  G. Anthoine, J.-G. Dumas, M. Hanling, M. de Jonghe, A. Maignan, C. Pernet, D. Roche
  USENIX Security'21
• Computing the Characteristic Polynomial of Generic Toeplitz-like and Hankel-like Matrices (hal:03189115, doi:10.1145/3452143.3465542)
  P. Karpman, C. Pernet, H. Signargout, G. Villard
  ISSAC'21
• Hermite Interpolation With Error Correction: Fields of Zero or Large Characteristic and Large Error Rate (pdf, doi:10.1145/3452143.3465525)
  E. Kaltofen, C. Pernet, Z-H. Yang
  ISSAC'21
• Deterministic computation of the characteristic polynomial in the time of matrix multiplication (arXiv:2010.04662, doi:10.1016/j.jco.2021.101572 slides)
  V. Neiger, C. Pernet
  J. of Complexity. (67). Dec. 2021
• Verification Protocols with Sub-Linear Communication for Polynomial Matrix Operations (hal:01829139, doi:10.1016/j.jsc.2020.06.006)
  D. Lucas, V. Neiger, C. Pernet, D. Roche, J. Rosenkilde
  J. of Symbolic Computation. 2021

2020

• Hermite Rational Function Interpolation with Error Correction. (pdf, doi:10.1007/978-3-030-60026-6_19)
  E. L. Kaltofen, C. Pernet, Z.-H. Yang
  CASC'20
• On fast multiplication of a matrix by its transpose. (hal:02432390, doi:10.1145/3373207.3404021, pdf@ACM, Slides)
  J.-G. Dumas, C. Pernet, A. Sedoglavic
  ISSAC'20
• Elimination-Based Certificates for Triangular Equivalence and Rank Profiles (doi:10.1016/j.jsc.2019.07.013, hal:02191075)
  J-G. Dumas, E. L. Kaltofen, D. Lucas, C. Pernet
  J. of Symbolic Computation (8). Spec. Issue on ISSAC'17. 2020

2019

• Improving the Complexity of Block Low-Rank Factorizations with Fast Matrix Arithmetic (doi:10.1137/19M1255628, hal:02008666)
  C.-P. Jeannerod, T. Mary, C. Pernet, D. Roche
  SIAM J. on Matrix Analysis and Applications (SIMAX). 40(4). 2019
• Secure Multi-Party Matrix Multiplication Based on Strassen-Winograd Algorithm (doi:10.1007/978-3-030-26834-3_5, hal:01781554)
  J-G. Dumas, P. Lafourcade, J. Fenner, D. Lucas, J.-B. Orfila, C. Pernet, M. Puys
  IWSEC'19. LNCS, Advances in Information and Computer Security, Volume 11689, pages 67--88, Springer 2019.
• LU factorization with errors (doi:10.1145/3326229.3326244, pdf@ACM, hal:01997592)
  J.-G. Dumas, J. van der Hoeven, C. Pernet, D. Roche
  ISSAC'19

2018

• Symmetric indefinite triangular factorization revealing the rank profile matrix (doi:10.1145/3208976.3209019, pdf@ACM, hal:01704793, arXiv-1802.10453, Slides)
  Jean-Guillaume Dumas, Clément Pernet
  ISSAC'18
• Time and space efficient generators for quasiseparable matrices (doi:10.1016/j.jsc.2017.07.010, hal:01424252)
  Clément Pernet, Arne Storjohann
  J. of Symbolic Computation (85), Special Issue on ISSAC'16, pp 224-246. March-Apr. 2018

2017

• Certificates for Triangular Equivalence and Rank Profiles (doi:10.1145/3087604.3087609, pdf@ACM, hal:01466093)
  Jean-Guillaume Dumas, David Lucas, Clément Pernet
  ISSAC'17.
• Early Termination in Parametric Linear System Solving and Rational Function Vector Recovery with Error Correction (doi:10.1145/3087604.3087645, pdf@ACM, pdf)
  Erich L. Kaltofen, Clément Pernet, Arne Storjohann, and Cleveland Waddell
  ISSAC'17.
• Fast Computation of the Rank Profile Matrix and the Generalized Bruhat Decomposition (doi:10.1016/j.jsc.2016.11.011, hal:01251223)
  Jean-Guillaume Dumas, Clément Pernet and Ziad Sultan
  J. of Symbolic Computation (83), Special Issue on ISSAC'15, pp 187-210. Dec. 2017

2016

• Recursion based parallelization of exact dense linear algebra routines for Gaussian elimination (hal:01084238, doi:10.1016/j.parco.2015.10.003)
  Jean-Guillaume Dumas, Thierry Gautier, Jean-Louis Roch, Clément Pernet and Ziad Sultan
  Parallel Computing (57), pp 235-249. Sept. 2016
• Computing with Quasiseparable Matrices (doi:10.1145/2930889.2930915, pdf@ACM, hal:01264131)
  Clément Pernet
  ISSAC'16

2015

• Computing the Rank Profile Matrix (pdf@ACM, hal:01107722)
  Jean-Guillaume Dumas, Clément Pernet and Ziad Sultan
  ISSAC'15. (Distinguished paper award)

2014

• Elements of Design for Containers and Solutions in the LinBox library (extended abstract)
  Brice Boyer, Jean-Guillaume Dumas, Pascal Giorgi, Clément Pernet and B. David Saunders
  ICMS'14
• Sparse polynomial interpolation codes and their decoding beyond half the minimum distance (doi:10.1145/2608628.2608660, pdf@ACM, revised pdf, arXiv:1403.3594)
  Erich L. Kaltofen and Clément Pernet
  ISSAC'14
• Parallel computation of echelon forms (hal, doi:10.1007/978-3-319-09873-9_42)
  Jean-Guillaume Dumas, Thierry Gautier, Clément Pernet and Ziad Sultan.
  EUROPAR'14

2013

• Simultaneous computation of the row and column rank profiles (doi:10.1145/2465506.2465517, pdf@ACM, arXiv, Slides)
  Jean-Guillaume Dumas, Clément Pernet and Ziad Sultan.
  ISSAC'13, June 2013
• Rank-profile revealing Gaussian elimination and the CUP matrix decomposition (S. Direct, pdf, arXiv)
  C-P. Jeannerod, C. Pernet and A. Storjohann
  Journal of Symbolic Computation. vol 56, Sept 2013.
• On decoding of quasi-BCH codes (hal archive)
  Morgan Barbier, Clément Pernet and Guillaume Quintin.
  WCC'13, Apr. 2013

2012

• Sparse Polynomial Interpolation and Berlekamp/Massey Algorithms That Correct Outlier Errors in Input Values (doi:10.1145/2442829.2442852, pdf@ACM, revised pdf,Slides)
  Matthew Comer, Erich Kaltofen and Clément Pernet.
  ISSAC'12, Jul 2012.

2010

• LinBox founding scope allocation, parallel building blocks, and separate compilation (pdf)
  Jean-Guillaume Dumas, Thierry Gautier, Clément Pernet and David Saunders
  Internation Congress on Mathematical Software, Kobe, Sept 13-17, 2010.
• Efficient Decomposition of Dense Matrices over GF(2) (arXiv)
  Martin Albrecht and Clément Pernet.
  Workshop on tools for Cryptanalysis, June 2010.
• Output sensitive decoding for redundant residue sytems (doi:10.1145/1837934.1837985"pdf@ACM)
  Majid Khonji, Clément Pernet, Jean-Louis Roch, Thomas Roche, and Thomas Stalinski.
  ISSAC'10, Jul 25, 2010.
• Fast computation of Hermite normal forms of random integer matrices, (doi:10.1016/j.jnt.2010.01.017,pdf)
  Clément Pernet and William Stein
  J. Number Theory (2010),

2009

• Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm (doi:10.1145/1576702.1576713, pdf@ACM, slides)
  Brice Boyer, Jean-Guillaume Dumas, Clément Pernet and Wei Zhou.
  ISSAC'09, Jul 28, 2009.
• On finding multiplicities of characteristic polynomial factors of black-box matrices (doi:10.1145/1576702.1576723, pdf@ACM, slides)
  Jean-Guillaume Dumas, Clément Pernet and David Saunders.
  ISSAC'09, Jul 28, 2009.

2008

• Dense Linear Algebra over Finite Fields: the FFLAS and FFPACK packages (doi:10.1145/1391989.1391992, pdf@ACM, arXiv )
  Jean-Guillaume Dumas, Pascal Giorgi and Clément Pernet
  Transaction on Mathematical Software.Vol. 35, num. 3, 34 pp, Nov. 2008.

2007

• Faster algorithms for the characteristic polynomial (doi:10.1145/1277548.1277590, pdf@ACM, slides)
  Clément Pernet and Arne Storjohann,
  ISSAC'07, jul. 29 - aug. 1 2007, Waterloo Ontario, Canada.

2006

• Adaptive Triangular System Solving (pdf)
  Jean-Guillaume Dumas, Jean-Louis Roch and Clément Pernet
  Dagstuhl Seminar Proceedings -- Challenges in Symbolic Comp. Soft. jul 2006, Dagstuhl, Germany.

2005

• Efficient Computation of the Characteristic Polynomial (doi:10.1145/1073884.1073905, pdf@ACM, arXiv, slides)
  Jean-Guillaume Dumas, Clément Pernet and Zhendong Wan
  ISSAC'05, jul. 24-27 2005, Beijing China.

2004

• FFPACK: Finite Field Linear Algebra Package (doi:10.1145/1005285.1005304, pdf@ACM, slides)
  Jean-Guillaume Dumas, Pascal Giorgi and Clément Pernet
  ISSAC'04, jul. 4-7, 2004, Santander España.

2002

• Finite Fields Linear Algebra Subroutines (doi:10.1145/780506.780515, pdf@ACM, Slides)
  Jean-Guillaume Dumas, Thierry Gautier and Clément Pernet
  ISSAC'02, jul. 7-10, 2002, Lille, France.

Posters

• Proofs of Retrievability with Low Server Storage (doi:10.1145/3319535.3363266, pdf@ACM)
  M. Hanling, G. Anthoine, J-G. Dumas, A. Maignan, C. Pernet, D. S. Roche
  ACM SIGSAC Conference on Computer and Communications CCS'19, Nov. 2019
• Secured Outsourced Linear Algebra
  Amrit Kumar, Clément Pernet and Jean-Louis Roch (hal:00926445)
  SafeComp 2013, sept 24-27. Toulouse, France
  
• LU based algorithms for the characteristic polynomial over a finite field (doi:10.1145/990353.990367", abstract@ACM, pdf)
  Clément Pernet and Zhendong Wan
  ISSAC'03, aug. 4-10 2003, Philadelphia, USA
  
• LUdivine: A Symbolic block LU factorisation for matrices over finite fields using BLAS (pdf)
  Morgan Brassel, Pascal Giorgi and Clément Pernet
  ECCAD'03: East Coast Computer Algebra Day, apt. 5, 2003, Clemson, USA
  

Dissertations

• High Performance and Reliable Algebraic Compting (Slides, tel-01094212)
  Habilitation à diriger des recherches Université J. Fourier, Grenoble 1. 21 Nov. 2014.
• Algèbre linéaire exacte efficace : le calcul du polynôme caractéristique (tel-00111346)
  PhD dissertation, University Joseph Fourier (Grenoble 1, France). sept. 27, 2006.
• Calcul du polynôme caractéristique sur des corps finis (ps.gz)
  Master thesis dissertation, University Joseph Fourier (Grenoble 1, France). jun. 30, 2003

Technical Reports

• Leading constants of rank deficient Gaussian elimination (hal-03976168)
  Clément Pernet, Hippolyte Signargout and Gilles Villard
  Tech report hal:03976168, 2023
• Efficient Dense Gaussian Elimination over the Finite Field with Two Elements (arXiv)
  M. Albrecht, G. Bard and C. Pernet
  arXiv:1111.6549v1 tech report. Nov 2011.
• Frobenius form in expected matrix multiplication time over sufficiently large fields (pdf)
  Clément Pernet and Arne Storjohann.
  Tech report, 2007.
• The report of my work during my first post-doctoral period at the Symbolic Computation Group at University of Waterloo, Ontario, Canada.
• Computing the Kalman form (arXiv)
  Rapport de recherche IMAG-ccsd-00009558, ArXiv:cs/0510014v4 [cs.SC], oct. 2005.
• Implementation of Winograd's algorithm over finite fields using ATLAS level 3 BLAS (ps.gz)
  Tech. report IMAG-ID

Talks

• Fast and accurate subcubic matrix multiplication(Slides)
  Workshop on Approximate Computing, Paris, Oct. 9, 2025.
• On the complexity of computing characteristic polynomials (Slides)
  Invited talk at RTCA'23: Fundamental Algorithms and Algorithmic Complexity, Paris. Sept 2023.
• Deterministic computation of the characteristic polynomial in the time of matrix multiplication (Slides)
  Aric Seminar, LIP, ENS de Lyon. Mars 2022.
• Computational exact linear algebra (Slides)
  Course at OSCAR Summer school on Computer Algebra. Sept. 2021.
• Deterministic computation of the characteristic polynomial in the time of matrix multiplication (Slides)
  JNCF'21 (online). Exposé joint avec Vincent Neiger. Mars 2021.
• On fast multiplication of a matrix by its transpose (Slides)
  ISSAC'20 (online.) Juillet 2020
• Calcul Formel et symbolique (Slides)
  Journée Histoire du Calcul. 80 ans du CNRS. LJK-Gricad, UGA. 2019
• Fast matrix arithmetic for rank structured matrices using non hierarchical representations (Slides)
  ILAS'19. Rio de Janeiro. July 8, 2019.
• Symmetric indefinite triangular factorization revealing the rank profile matrix (Slides)
  ISSAC'18. New-York, NY. USA. July 17, 2018.
• Task based parallelization of recursive linear algebra routines using Kaapi (Slides)
  Exposé à la Journée Runtime (groupe Calcul du CNRS). Inria Paris, Jan. 20, 2017.
• Smaller and faster generators for quasiseparable matrices (Slides)
  CASYS Seminar. Laboratoire Jean Kuntzmann, Université Grenoble Alpes. Nov. 10, 2016.
• Sparse interpolation and error correcting codes (Slides)
  MICA'16. Waterloo, ON, Canada. July 18, 2016.
• High performance computer algebra: how to use floating point arithmetic exactly? (Slides)
  RAIM'16. Banyuls, France. June 29, 2016.
• Computing the Rank Profile Matrix (Slides)
  AriC Seminar. Lab. de l'Informatique du Parallélisme, ENS de Lyon. Oct. 8, 2015.
• High Performance Computer Algebra: how to use floating point arithmetic axactly?
  Journée recherche informatique et calcul. Lab. de l'Informatique du Parallélisme, Lyon. Sept. 29, 2015.
• Exact Linear Algebra Algorithmic: Theory and Practice ( pdf@ACM, Slides)
  Tutorial presentation at ISSAC '15. Bath, UK. Jul. 6-9, 2015.
• Parallel Computation of Echelon Forms and Rank Profiles (Slides)
  Minisymposium on High Performance Symbolic Computation.
  SIAM conf. on Parallel Processing for Scientific Computing. Portland, OR, USA. Feb. 18-21, 2014.
• (Sparse) Interpolation with Outliers (Slides)
  Minisymposium on Sparse models, interpolation and polynomials.
  SIAM meeting on Applied Algebraic Geomety 2013. Fort Collins, CO, USA. Aug 1-4, 2013.
• Simultaneous computation of the row and column rank profiles
  Minisymposium on Exact Linear Algebra Algorithms
  SIAM meeting on Applied Algebraic Geomety 2013. Fort Collins, CO, USA. Aug 1-4, 2013.
• Adaptive decoding for dense and sparse evaluation/interpolation codes (pdf)
  Séminaire Calcul formel et Codes, IRMAR, Rennes, 23 novembre. 2012.
• Computing canonical forms in exact linear algebra (pdf)
  Plenary lecture at ECRYPT II Summer School on Tools, Mykonos, Greece, June 1st. 2012.
• Parallel programming tools for exact linear algebra (pdf)
  Plenary lecture at ECRYPT II Summer School on Tools, Mykonos, Greece, June 1st. 2012.
• Adaptive decoding for evaluation/interpolation codes
  Séminaire Codage Cryptologie et Algorithmes, IHP, UPMC, Paris Fev 3rd, 2012.
• Elimination and echelon forms in exact linear algebra
  SIAM workshop on Applied Algebraic Geometry, NCSU, Raleigh, NC, USA., Oct 7, 2011.
• Elimination and echelon forms in exact linear algebra (pdf)
  Invited talk at the East Coast Computer Algebra Day, U of Waterloo, ON, Canada, Apr 9, 2011.
• Adaptive decoding for evaluation/interpolation codes (pdf)
  Algebra Seminar, C. Shannon Institure, UC Dublin, Ireland, June 3rd, 2010.
• Décodage adaptatif pour les systèmes multimodulaires redondants (pdf)
  Journées nationales du Calcul Formel, 3-7 Mai 2010, CIRM Luminy, France.
• Décodage adaptatif pour les systèmes multimodulaires redondants (pdf)
  Séminaire du Groupe de Travail ARENAIRE, LIP, ENS-Lyon, 25 Mars 2010.
• Calcul efficace de la forme normale de Hermite de matrices entières (pdf)
  Séminaire du projet ALGORITHMS, INRIA Rocquencourt, 11 Janvier 2010.
• Parallel adaptive computing with Kaapi middleware (pdf)
  Second workshop of the joint laboratory for petascale computing, Urbana Champaign, IL, USA, Dec 2, 2009.
• Exact linear algebra tools for computer assisted proofs (pdf)
  Dagstuhl Seminar, Dagstuhl Germany, Nov 19, 2009.
• Calcul intensif, algèbre linéaire exact et applications (pdf)
  1ère journée du GDR Calcul, Institut Henri Poincaré, Paris, Nov 10, 2009.
• The LinBox library (pdf)
  Combinatorial and Algebraic Topology Workshop, Sandia Labs, Santa Fe, NM, USA. Aug 29, 2009.
• Computing exactly with unsafe resources: fault tolerant exact linear algebra and cloud computing (pdf)
  Sage Days 16, Universitat Politècnica de Catalunya, Barcelona, Spain. June 23, 2009.
• Design perspectives for exact linear algebra libraries (pdf)
  Number Theory and computation seminar, U. of Washington, Seattle, WA, USA. Nov. 13, 2008.
• Efficient Exact Linear Algebra over GPU (pdf)
  Sage Days 9, Simon Fraser University, Burnaby, Canada, aug. 15, 2008.
• What can you compute exactly whith floating point linear algebra. (pdf)
  Sage Seminar, University of Washington, Dept. of Mathematics, jan. 24, 2008.
• Algèbre linéaire dense dans des petits corps finis: théorie et pratique.
  Séminaire CACAO, INRIA-LORIA, Nancy, nov. 29, 2007.
• Algèbre linéaire dense dans des petits corps finis: théorie et pratique.
  Groupe de travail ARENAIRE, LIP-ENS, Lyon, nov. 28, 2007.
• Fast exact linear algebra: LinBox (pdf)
  Sage Days 6, Universty of Bristol, UK, nov. 11, 2007.
• Matrix multiplication based computations of the characteristic polynomial
  Seminar at the University of Calgary, Canada, oct. 31, 2007.
• Recent advances in exact linear algebra
  Seminar of Algorithms and Complexity, University of Toronto, dpt. of Mathematics, oct. 15, 2007.
• Matrix multiplication based exact linear algebra: how asymptotic and practical efficiency meet
  SAGE Days 3, IPAM-UCLA, Los Angeles, USA, feb. 2007
• Matrix multiplication based computations of the characteristic polynomial (pdf)
  ORCCA Joint lab. meeting, University of Western Ontario, London, Canada, feb. 2007
• Parallel perspectives for the LinBox library ( pdf)
  Interactive Parallel Computation, MSRI workshop, Berkeley, USA, jan 2007
• Algorithmique dense pour le calcul du polynome caractéristique
  Journées nationales du calcul formel, Luminy, nov 2005
• Calcul du polynome caractéristique sur des corps finis
  Ecole jeunes chercheurs en algorithmique et calcul formel, Grenoble, apr 2004
• Etude du conditionnement de classes de matrices complexes (pdf)
  Fall meeting of the laboratory of modelisation and computation, Sept 2004.
  
• Algorithmes probabilistes : application en cryptographie et en algèbre linéaire
  Séminaire compréhensible Institut Fourier - Lab. de Modélisation et Calcul, jan 2003