2 PhD students (Supervision / Co-supervision)

• FERRO Quentin : Precision Auto-Tuning and Numerical Validation
• LESNOFF Dimitri : Efficient linear algebra on GPUs for Gr√∂bner bases computations

4 PhD graduated 2012 - 2019

2006-2023 Publications

• 2023
  • R. Molina, S. Graillat, F. Jézéquel, Th. Mary : “Adaptive Precision Sparse Iterative Solvers”, SIAM Conference on Computational Science and Engineering (CSE23), Amsterdam, Netherlands (2023)
  • K. Li, K. He, S. Graillat, H. Jiang, T. Gu, J. Liu : “Multi-level parallel multi-layer block reproducible summation algorithm”, Parallel Computing, vol. 115, pp. 102996, (Elsevier) (2023)
• 2022
  • R. Molina, S. Graillat, F. Jézéquel, Th. Mary : “Adaptive Precision Sparse Matrix-Vector Product and its application to Krylov Solvers”, 13^es Rencontres Arithmétique de l'Informatique Mathématique (RAIM 2022), Nantes, France (2022)
  • Q. Ferro, S. Graillat, Th. Hilaire, F. Jézéquel, B. Lewandowski : “Neural Network Precision Tuning Using Stochastic Arithmetic”, RAIM 2022 : 13^es Rencontres Arithmétique de l'Informatique Mathématique, Nantes, France (2022)
  • S. Graillat, F. Jézéquel, Th. Mary, R. Molina : “Adaptive precision sparse matrix-vector product and its application to Krylov solvers”, (2022)
  • Q. Ferro, S. Graillat, Th. Hilaire, F. Jézéquel, B. Lewandowski : “Neural Network Precision Tuning Using Stochastic Arithmetic”, NSV'22, 15^th International Workshop on Numerical Software Verification,, Haifa, Israel (2022)
  • R. Molina, S. Graillat, F. Jézéquel, Th. Mary : “Adaptive Precision Sparse Matrix-Vector Product and its Application to Krylov Solvers”, Sparse Days Meeting 2022, Saint-Girons, France (2022)
  • Q. Ferro, S. Graillat, Th. Hilaire, F. Jézéquel, B. Lewandowski : “Neural Network Precision Tuning Using Stochastic Arithmetic”, Sparse Days conference, Saint-Girons, France (2022)
  • X. Lei, T. Gu, S. Graillat, H. Jiang, J. Qi : “A Fast Parallel High-Precision Summation Algorithm Based on AccSumK”, Journal of Computational and Applied Mathematics, vol. 406, pp. 113827, (Elsevier) (2022)
  • Th. Cameron, S. Graillat : “On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots”, Electronic Transactions on Numerical Analysis, vol. 55, pp. 401–423, (Kent State University Library) (2022)
• 2021
  • S. Graillat, F. Jézéquel, E. Queiros Martins, M. Spyropoulos : “Computing multiple roots of polynomials in stochastic arithmetic with Newton method and approximate GCD”, International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2021), Timisoara, Romania (2021)
  • R. Iakymchuk, S. Graillat, J. Aliaga : “General framework for deriving reproducible Krylov subspace algorithms: A BiCGStab case study”, (2021)
  • R. Iakymchuk, D. Mukunoki, T. Ogita, K. Ozaki, S. Graillat : “Accurate and Reproducible Conjugate Gradient in Hybrid Parallel Environments”, (2021)
  • F. Jézéquel, S. Graillat, D. Mukunoki, T. Imamura, R. Iakymchuk : “Fast rounding error estimation for compute-intensive operations using standard floating-point arithmetic”, RAIM (Rencontres Arithmétiques de l'Informatique Mathématique), Paris, France (2021)
• 2020
  • S. Graillat, F. Jézéquel : “Tight interval inclusions with compensated algorithms”, IEEE Transactions on Computers, vol. 69 (12), pp. 1774-1783, (Institute of Electrical and Electronics Engineers) (2020)
  • R. Iakymchuk, M. Vayá, S. Graillat, J. Aliaga, E. Quintana‑Ortí : “Reproducibility of parallel preconditioned conjugate gradient in hybrid programming environments”, International Journal of High Performance Computing Applications, vol. 34 (5), pp. 502-518, (SAGE Publications) (2020)
  • F. Jézéquel, S. Graillat, D. Mukunoki, T. Imamura, R. Iakymchuk : “Can we avoid rounding-error estimation in HPC codes and still get trustworthy results?”, Lecture Notes in Computer Science, Los Angeles, CA, United States (2020)
  • S. Graillat, V. Lefèvre, J.‑M. Muller : “Alternative Split Functions and Dekker’s Product”, Proceedings of ARITH-2020, IEEE 27^th Symposium on Computer Arithmetic, Portland, United States, pp. 1-7, (IEEE) (2020)
  • R. Iakymchuk, M. Barreda, S. Graillat, J. Aliaga, E. Quintana‑Ortí : “Reproducibility of Parallel Preconditioned Conjugate Gradient in Hybrid Programming Environments”, (2020)
  • F. Jézéquel, S. Graillat, D. Mukunoki, T. Imamura, R. Iakymchuk : “Can we avoid rounding-error estimation in HPC codes and still get trustful results?”, (2020)
  • T. Boku, N. Fujita, S. Graillat, J. Huthmann, R. Iakymchuk, T. Imamura, F. Jézéquel, A. Koshiba, D. Mukunoki, K. Sano, Y. Tan : “Minimal-Precision Computing for High-Performance, Energy-Efficient, and Reliable Computations”, 2^nd R-CCS international symposium, K to Fugaku: Simulation, Big Data and AI supporting Society 5.0, Kobe, Japan (2020)
  • R. Iakymchuk, S. Graillat, F. Jézéquel, D. Mukunoki, T. Imamura, Y. Tan, A. Koshiba, J. Huthmann, K. Sano, N. Fujita, T. Boku : “Optimizing Precision for High-Performance, Robust, and Energy-Efficient Computations”, International Conference on High Performance Computing in Asia-Pacific Region,, Fukuoka, Japan (2020)
• 2019
  • T. Boku, N. Fujita, S. Graillat, J. Huthmann, R. Iakymchuk, T. Imamura, F. Jézéquel, A. Koshiba, D. Mukunoki, K. Sano, Y. Tan : “Minimal-Precision Computing for High-Performance, Energy-Efficient, and Reliable Computations”, International Conference on High Performance Computing, Networking, Storage and Analysis (SC19), Denver, United States (2019)
  • T. Imamura, D. Mukunoki, R. Iakymchuk, F. Jézéquel, S. Graillat : “Numerical Reproducibility based on Minimal-Precision Validation”, Computational Reproducibility at Exascale Workshop (CRE2019), in conjunction with the International Conference on High Performance Computing, Networking, Storage and Analysis (SC19), Denver, United States (2019)
  • D. Mukunoki, I. Toshiyuki, Y. Tan, A. Koshiba, J. Huthmann, K. Sano, F. Jézéquel, S. Graillat, R. Iakymchuk, N. Fujita, T. Boku : “Minimal-Precision Computing for High-Performance, Energy-Efficient, and Reliable Computations”, France-Japan-Germany trilateral workshop: Convergence of HPC and Data Science for Future Extreme Scale Intelligent Applications, Tokyo, Japan (2019)
  • R. Iakymchuk, S. Graillat, D. Defour, E. Quintana‑Ortí : “Hierarchical approach for deriving a reproducible unblocked LU factorization”, International Journal of High Performance Computing Applications, pp. #1094342019832968, (SAGE Publications) (2019)
  • S. Graillat, F. Jézéquel, R. Picot, F. Févotte, B. Lathuilière : “Auto-tuning for floating-point precision with Discrete Stochastic Arithmetic”, Journal of computational science, vol. 36, pp. 101017, (Elsevier) (2019)
• 2018
  • S. Graillat : “An accurate algorithm for evaluating rational functions”, Applied Mathematics and Computation, vol. 337, pp. 494-503, (Elsevier) (2018)
  • S. Graillat, F. Jézéquel : “Tight interval inclusions with compensated algorithms”, 18^th international symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2018), 18^th international symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2018), Book of Abstracts, Tokyo, Japan, pp. 86-87 (2018)
  • S. Graillat, F. Jézéquel, R. Picot : “Numerical Validation of Compensated Algorithms with Stochastic Arithmetic”, Applied Mathematics and Computation, vol. 329, pp. 339-363, (Elsevier) (2018)
  • S. Graillat, F. Jézéquel, R. Picot, F. Févotte, B. Lathuilière : “Numerical validation in quadruple precision using stochastic arithmetic”, TNC'18. Trusted Numerical Computations, vol. 8, Kalpa Publications in Computing, Krakow, Poland, pp. 38-53, (EasyChair) (2018)
• 2017
  • R. Iakymchuk, S. Graillat, D. Defour, E. Laure, E. Quintana‑Ortí : “Towards a Reproducible Solution of Linear Systems”, Supercomputing Conference 2017-Computational Reproducibility at Exascale Workshop, Denver, United States (2017)
  • S. Boldo, S. Graillat, J.‑M. Muller : “On the robustness of the 2Sum and Fast2Sum algorithms”, ACM Transactions on Mathematical Software, vol. 44 (1), (Association for Computing Machinery) (2017)
  • R. Iakymchuk, E. Quintana‑Ortí, E. Laure, S. Graillat : “Towards Reproducible Blocked LU Factorization”, 4^th International Workshop on Reproducibility in Parallel Computing in conjunction with IPDPS 2017 - 31^st IEEE International Parallel & Distributed Processing Symposium, Orlando, United States (2017)
  • L. Abbas‑Turki, S. Graillat : “Resolution of a large number of small random symmetric linear systems in single precision arithmetic on GPUs”, Journal of Supercomputing, vol. 73 (4), pp. 1360-1386, (Springer Verlag) (2017)
  • S. Graillat : “Accurate computations with polynomials”, The International Workshop on Numerical Verification and its Applications, Miyako-jima, Okinawa, Japan (2017)
  • S. Graillat, Y. Ibrahimy, C. Jeangoudoux, Ch. Lauter : “A Parallel Compensated Horner Scheme”, CSE 2017, SIAM Conference on Computational Science and Engineering (CSE), Atlanta, United States (2017)
  • S. Graillat, C. Jeangoudoux, Ch. Lauter : “MPDI: A Decimal Multiple-Precision Interval Arithmetic Library”, Reliable Computing Journal, vol. 25, Volume 25 (Special volume containing refereed papers from SCAN 2016), pp. 38-52 (2017)
• 2016
  • P. Fortin, M. Gouicem, S. Graillat : “GPU-Accelerated Generation of Correctly Rounded Elementary Functions”, ACM Transactions on Mathematical Software, vol. 43 (3), pp. 22:1-22:26, (Association for Computing Machinery) (2016)
  • R. Iakymchuk, S. Graillat, D. Defour, E. Quintana‑Ortí : “Hierarchical Approach for Deriving a Reproducible LU factorization on GPUs”, The Numerical Reproducibility at Exascale (NRE16) workshop held as part of the Supercomputing Conference (SC16), Salt Lake City, UT, United States (2016)
  • S. Graillat, F. Jézéquel, M. Ibrahim : “Dynamical control of Newton’s method for multiple roots of polynomials”, Reliable Computing Journal, vol. 21 (2016)
  • S. Graillat, C. Jeangoudoux, Ch. Lauter : “A Decimal Multiple-Precision Interval Arithmetic Library”, book of abstracts : 17^th International Symposium on Scientific Computing, Computer Arithmetics and Verified Numerics., Uppsala, Sweden (2016)
  • S. Graillat, F. Jézéquel, R. Picot, F. Févotte, B. Lathuilière : “PROMISE: floating-point precision tuning with stochastic arithmetic”, 17^th international symposium on Scientific Computing, Computer Arithmetic and Verified Numerics (SCAN 2016), UPPSALA, Sweden, pp. 98-99 (2016)
  • R. Iakymchuk, I. Toshiyuki, S. Graillat, S. Markidis, E. Laure : “A Case Study of the Reproducibility Issues in EigenExa”, EASC2016, Exascale Applications and Software Conference, Stockholm, Sweden (2016)
  • R. Iakymchuk, D. Defour, C. Collange, S. Graillat : “Reproducible and Accurate Algorithms for Numerical Linear Algebra”, SIAM Conference on Parallel Processing for Scientific Computing (PP16), Paris, France, (SIAM) (2016)
  • H. Jiang, S. Graillat, R. Barrio, C. Yang : “Accurate, validated and fast evaluation of elementary symmetric functions and its application”, Applied Mathematics and Computation, vol. 273, pp. 1160-1178, (Elsevier) (2016)
  • R. Iakymchuk, D. Defour, S. Graillat : “Towards Fast, Accurate and Reproducible LU Factorization”, SCAN 2016, 17^th international symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, Uppsala, Sweden, pp. 59-60 (2016)
  • L.A. Abbas‑Turki, S. Graillat : “Resolution of a large number of small random symmetric linear systems in single precision arithmetic on GPUs”, International conference on Monte-Carlo techniques, Paris, France, pp. 25 (2016)
  • R. Iakymchuk, D. Defour, C. Collange, S. Graillat : “Reproducible and Accurate Matrix Multiplication”, 16^th International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics n°9553, Lecture Notes of Computer Science, Wurzburg, Germany, pp. 126-137 (2016)
• 2015
  • S. Graillat, F. Jézéquel, R. Picot : “Numerical Validation of Compensated Summation Algorithms with Stochastic Arithmetic”, 8^th International Workshop on Numerical Software Verification, NSV 2015, vol. 317, Electronic Notes in Theoretical Computer Science, Seattle, United States, pp. 55-69, (Elsevier) (2015)
  • C. Collange, D. Defour, S. Graillat, R. Iakymchuk : “Numerical Reproducibility for the Parallel Reduction on Multi- and Many-Core Architectures”, Parallel Computing, vol. 49, pp. 83-97, (Elsevier) (2015)
  • S. Graillat, V. Lefèvre, J.‑M. Muller : “On the maximum relative error when computing integer powers by iterated multiplications in floating-point arithmetic”, Numerical Algorithms, vol. 70 (3), pp. 653-667, (Springer Verlag) (2015)
  • S. Graillat, Ch. Lauter, P. Peter Tang, N. Yamanaka, Sh. Oishi : “Efficient Calculations of Faithfully Rounded l2-Norms of n-Vectors”, ACM Transactions on Mathematical Software, vol. 41 (4), pp. 24:1, (Association for Computing Machinery) (2015)
  • C. Collange, D. Defour, S. Graillat, R. Iakymchuk : “Numerical Reproducibility for the Parallel Reduction on Multi- and Many-Core Architectures”, (2015)
  • R. Iakymchuk, D. Defour, C. Collange, S. Graillat : “Reproducible Triangular Solvers for High-Performance Computing”, 2015 12^th International Conference on Information Technology - New Generations, Las Vegas, NV, United States, pp. 353-358, (IEEE) (2015)
  • R. Iakymchuk, S. Graillat, C. Collange, D. Defour : “ExBLAS: Reproducible and Accurate BLAS Library”, RAIM: Rencontres Arithmétiques de l’Informatique Mathématique, Rennes, France (2015)
  • R. Iakymchuk, D. Defour, C. Collange, S. Graillat : “Reproducible and Accurate Matrix Multiplication for GPU Accelerators”, (2015)
  • R. Iakymchuk, C. Collange, D. Defour, S. Graillat : “ExBLAS: Reproducible and Accurate BLAS Library”, NRE: Numerical Reproducibility at Exascale, Austin, TX, United States (2015)
  • R. Iakymchuk, C. Collange, D. Defour, S. Graillat : “Reproducibility and Accuracy for High-Performance Computing”, 7^e Rencontre Arithmétique de l'Informatique Mathématique, Rennes, France (2015)
• 2014
  • S. Graillat, Ch. Lauter, P. Peter Tang, N. Yamanaka, Sh. Oishi : “A method of calculating faithful rounding of l2-norm for n-vectors”, Proceedings of the 16^th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computation (SCAN), Wuerzburg, Germany, pp. 60-61 (2014)
  • C. Collange, D. Defour, S. Graillat, R. Iakymchuk : “Reproducible and Accurate Matrix Multiplication for High-Performance Computing”, 16^th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, Wuerzburg, Germany, pp. 42-43 (2014)
  • C. Collange, D. Defour, S. Graillat, R. Iakymchuk : “A Reproducible Accurate Summation Algorithm for High-Performance Computing”, SIAM Workshop on Exascale Applied mathematics Challenges and opportunites, Chicago, United States (2014)
• 2013
  • S. Graillat : “Contribution to the increase of accuracy and validation of numerical algorithms”, habilitation, defence 12/02/2013 (2013)
  • H. Jiang, S. Graillat, C. Hu, Sh. Lia, X. Liao, L. Cheng, F. Su : “Accurate evaluation of the $k$-th derivative of a polynomial”, Journal of Computational and Applied Mathematics, vol. 243, pp. 28-47, (Elsevier) (2013)
  • H. Jiang, S. Graillat, R. Barrio : “Accurate and Fast Evaluation of Elementary Symmetric Functions”, 21^st IEEE Symposium on Computer Arithmetic, ARITH 2013, Austin, TX, United States, pp. 183-190, (IEEE) (2013)
• 2012
  • P. Fortin, M. Gouicem, S. Graillat : “Solving the Table Maker’s Dilemma by reducing divergence on GPU”, Proceedings of the 15^th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerical Computations, Novosibirsk, Russian Federation, pp. 45-46 (2012)
  • S. Graillat, V. Ménissier‑Morain : “Accurate summation, dot product and polynomial evaluation in complex floating point arithmetic”, Information and Computation n°216, pp. 57-71, (Elsevier) (2012)
  • P. Fortin, M. Gouicem, S. Graillat : “Towards solving the Table Maker’s Dilemma on GPU”, 20^th Euromicro International Conference on Parallel, Distributed and Network-Based Processing, Garching, Germany, pp. 407-415, (IEEE Computer Society) (2012)
• 2011
  • S. Graillat, F. Jézéquel, Sh. Wang, Y. Zhu : “Stochastic Arithmetic in Multiprecision”, Mathematics in Computer Science, vol. 5 (4), pp. 359-375, (Springer) (2011)
• 2010
  • S. Graillat, F. Jézéquel, Y. Zhu : “SAM: a multiprecision stochastic arithmetic library”, 14^th international symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2010), Lyon, France, pp. 70-71 (2010)
  • S. Graillat, F. Jézéquel, Y. Zhu : “Stochastic Arithmetic in Multiprecision”, Third International Workshop on Numerical Software Verification (NSV-3), part of Federated Logic Conference (FLoC), Edinburgh, United Kingdom (2010)
  • J. Jean, S. Graillat : “Fast dot product over finite field”, (2010)
• 2009
  • S. Graillat, Ph. Trébuchet : “A new algorithm for computing certified numerical approximations of the roots of a zero-dimensional system”, ISSAC'09 - Proceedings of the 2009 international symposium on Symbolic and algebraic computation, Seoul, Korea, Republic of, pp. 167-173, (ACM) (2009)
  • S. Graillat : “Accurate Floating Point Product and Exponentiation”, IEEE Transactions on Computers, vol. 58 (7), pp. 994-1000, (Institute of Electrical and Electronics Engineers) (2009)
  • S. Graillat, Ph. Langlois, N. Louvet : “Algorithms for Accurate, Validated and Fast Polynomial Evaluation”, Japan Journal of Industrial and Applied Mathematics, vol. 26 (2-3), pp. 191-214, (Kinokuniya Company) (2009)
  • H. Nguyen, S. Graillat, J.‑L. Lamotte : “Extended precision with a rounding mode toward zero environment. Application on the CELL processor”, International Journal of Reliability and Safety, vol. 3 (1-3), pp. 153-173, (Inderscience) (2009)
  • J.‑M. Chesneaux, S. Graillat, F. Jézéquel : “Rounding errors”, chapter in Wiley Encyclopedia of Computer Science and Engineering (Benjamin Wah, ed.), vol. 4, pp. 2490-2494, (ISBN: 978-0-471-38393-2) (2009)
• 2008
  • S. Graillat : “Accurate simple zeros of polynomials”, 13^th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerical Computations SCAN'08, El Paso, Texas, United States, pp. 52-53 (2008)
  • S. Graillat, J.‑L. Lamotte, Siegfried M. Rump, S. Markov : “Interval arithmetic on the Cell processor”, 13^th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerical Computations SCAN'08, El Paso, Texas, United States, pp. 54-54 (2008)
  • S. Graillat : “Accurate simple zeros of polynomials in floating point arithmetic”, Computers & Mathematics with Applications, vol. 56 (4), pp. 1114-1120, (Elsevier) (2008)
  • S. Graillat, V. Ménissier‑Morain : “Compensated Horner scheme in complex floating point arithmetic”, Proceedings, 8^th Conference on Real Numbers and Computers, Santiago de Compostela, Spain, pp. 133-146 (2008)
  • S. Graillat : “Accurate Floating Point Product”, Proceedings of the Workshop on Reliable Engineering Computing, Savannah, Georgia, United States, pp. 351-361 (2008)
  • H. Nguyen, S. Graillat, J.‑L. Lamotte : “Precise and effective scientific calculation on the CELL processor”, Proceedings of the Workshop on Reliable Engineering Computing, Savannah, Georgia, United States, pp. 333-350 (2008)
  • S. Graillat, J.‑L. Lamotte, H. Nguyen : “Error-Free Transformation in Rounding Mode toward Zero”, Numerical Validation in Current Hardware Architectures, revised papers, vol. 5492, Lecture Notes In Computer Science, Dagstuhl, Germany, pp. 217-229, (Springer) (2008)
  • S. Graillat : “Some topological and geometric properties of pseudozero set”, Applied Mathematics E - Notes, vol. 8, pp. 98-108, (Tsing Hua University) (2008)
• 2007
  • S. Graillat : “Pseudozero Set of Real Multivariate Polynomials”, Mathematics in Computer Science, vol. 1 (2), pp. 337-352, (Springer) (2007)
  • S. Graillat, V. Ménissier‑Morain : “Error-Free Transformations in Real and Complex Floating Point Arithmetic”, Proceedings of International Symposium on Nonlinear Theory and its Applications (NOLTA'07), Vancouver, Canada, pp. 341-344 (2007)
  • S. Graillat, Ph. Langlois : “Real and complex pseudozero sets for polynomials with applications”, RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), vol. 41 (1), pp. 45-56, (EDP Sciences) (2007)
• 2006
  • S. Graillat : “Validated Pseudozero Set of Polynomials”, 12^th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, Duisburg, Germany, Duisburg, Germany, pp. 160-161, (IEEE) (2006)
  • S. Graillat, Ph. Langlois, N. Louvet : “Choosing a twice more accurate dot product implementation”, 4^th International Conference of Numerical Analysis and Applied Mathematics, Hersonnisos, Crete, Greece, pp. 498-499 (2006)