Gérard Meurant



Professional address : retired from CEA

E-mail : gerard.meurant@gmail.com, gerard.meurant@wanadoo.fr

Education

Maitrise de Mathématiques, Université Paris XI, 1970

Diplome d'Etudes Approfondies de Mathématiques, Université Paris XI, 1971

Thèse de 3ème cycle de Mathématiques, Université Paris XI, advisor R. Temam, 1972

Professional experience

1970-73 Part time position at Commissariat à l'Energie Atomique (CEA), Centre d'Etudes de Saclay, Computer Center.

1974-77 Engineer with Compagnie Internationale de Services en Informatique (CISI)

1977-2008 Engineer at CEA

2003-2008 Research Director at CEA

2008 (Feb 1rst) Retirement from CEA



Dec 1981-Aug 1982 visiting scientist, Computer Science Dept, Stanford University, USA.

1984-1995 Lecturer at Université Paris VI, DEA d'Analyse numérique

June 2-July 8 1984, visiting scientist, Applied Math group, Lawrence Berkeley Lab, USA.

July 17-Aug 18 1985, visiting scientist, Computer Science Dept, Stanford University, USA.

Sept 28-Oct 11 1986 visiting scientist, Mathematics Inst. Catholic University of Nijmegen (Netherlands).

winter 1987 visiting scientist, Computer Science Dept, Stanford University, USA.

July 1989, visiting scientist, Computer Science Dept, Stanford University, USA.

February 2004, visitor at Computer Science Dept, Stanford University, USA.

April 2005, visitor at Computer Science Dept, Stanford University, USA.

March 2007, visitor at Computer Science Dept, Stanford University, USA.

April 2008, visitor at Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic.

April-May 2009, October-November 2009, working at Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic.

October-November 2010, visiting scientist Necas Center, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic.

October-November 2011, visitor at Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic.

January-April 2012, CARIPARO visiting professor, Department of Mathematics, University of Padua, Italy.

September 2012, visitor at Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic.

November-December 2013, visitor at Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic.

April 2014, visitor at Department of Mathematics, University of Padua, Italy.

September 2014, visitor at Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic.

March 2016, visitor at Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic.

July 2017, visitor at Department of Numerical Mathematics, Charles University, Prague, Czech Republic.

June 2017, visitor at Department of Mathematics, University of Padua, Italy.

September 2018, visitor at Department of Numerical Mathematics, Charles University, Prague, Czech Republic.

September 2022, visitor at Department of Numerical Mathematics, Charles University, Prague, Czech Republic.

September 2023, visitor at Department of Numerical Mathematics, Charles University, Prague, Czech Republic.

August 2024, visitor at Department of Numerical Mathematics, Charles University, Prague, Czech Republic.

Awards

Prix CEA 1988

Cray Gigaflops Award 1990

Palmes Académiques 1995

Memberships

SMAI Société de Mathématiques Appliquées et Industrielles (French applied math society).

GAMNI/SMAI Groupe pour l'Avancement des Méthodes Numériques de l'Ingénieur.

SIAM (Society for Industrial and Applied Math Society).

Professional Activities

Advisory board, International Journal of High Performance Computing Applications 1987-?

Editor, SIAM Journal on Scientific Computing 1989-1999

Editor, International Journal of High Speed Computing 1989-2020

Editor, Numerical Algorithms 1992-

SMAI (Société de Mathématiques Appliquées et Industrielles) secretary 1987-89

SMAI council member 1984-1991

GAMNI treasurer 1985-1990

Local organizing committee FICIAM 1987

Member of the CERFACS Scientific Council 2005--2009

Books

  • G. MEURANT & G.H. GOLUB, Résolution numérique des grands systèmes linéaires. Eyrolles, Paris (1983), in french.

  • R. GLOWINSKI, G.H. GOLUB, G. MEURANT & J. PERIAUX Eds., Proceedings of the first international symposium on domain decomposition methods for partial differential equations. SIAM (1988).

  • R. GLOWINSKI, Y. KUZNETSOV, G. MEURANT, J. PERIAUX & O. WIDLUND Eds., Proceedings of the fourth international symposium on domain decomposition methods for partial differential equations. SIAM (1991).

  • D. KEYES, T. CHAN, G. MEURANT, J. SCROGGS & R. VOIGT Eds, Proceedings of the fifth international symposium on domain decomposition methods for partial differential equations. SIAM (1992).

  • G. MEURANT, Computer solution of large linear systems. North-Holland (1999).

  • G. MEURANT, The Lanczos and Conjugate Gradient algorithms, from theory to finite precision computations. SIAM (2006).

  • G.H. GOLUB & G. MEURANT, Matrices, moments and quadrature with applications. Princeton University Press (2010).

  • G. MEURANT & J. DUINTJER TEBBENS, Krylov methods for nonsymmetric linear systems, Springer (2020).

  • C. BREZINSKI, G. MEURANT & M. REDIVO-ZAGLIA, A journey through the history of numerical linear algebra, SIAM (2022)

  • G. MEURANT & P. TICHY, Error norm estimation in the conjugate gradient algorithm, SIAM (2024)

    Papers in Journals (to download some recent papers, see Publications)

  • Utilisation de la méthode du gradient conjugué sur calculateurs vectoriels; comparaisons Cray 1-S, CDC Cyber 205. Bulletin de l'INRIA, n 94 (1984) pp 31-34.

  • The block preconditioned conjugate gradient method on vector computers. BIT v 24 (1984) pp 623-633.

  • The conjugate gradient method on supercomputers. Supercomputer v 13 (1986) pp 9-17.

  • Multitasking the conjugate gradient method on the CRAY X-MP/48. Parallel Computing 5 (1987) pp 267-280.

  • Domain decomposition preconditioners for the conjugate gradient method. Calcolo v 25 n 1-2 (1988) pp 103-119.

  • Practical use of the conjugate gradient method on parallel supercomputers. Computer Physics Com. v 53 (1989) pp 467-477.

  • Domain decomposition methods for partial differential equations on parallel computers. Int. J. of Supercomputer Appl. v 2 n 4 (1989) pp 5-12.

  • Iterative methods for multiprocessor vector computers. Computer Physics Reports v 11 (1989) pp 51-80.

  • A domain decomposition method for parabolic problems. Applied Numerical Mathematics v 8 (1991) pp 427-441.

  • A review on the inverse of tridiagonal and block tridiagonal symmetric matrices. SIAM J. of Matrix Anal. and Appl v 13 n 3 (1992) pp 707-728.

  • Os computadores paralelos e o futuro da computaçao cientifica. Boletim da SBMAC (Sociedade Brasileira de Matematica Aplicada e computational) v 3 n 1 (1992) pp 36-52.

  • The computation of bounds for the norm of the error in the conjugate gradient algorithm. Numerical Algorithms, v 16 n 1 (1998) pp 77-87.

  • Numerical experiments in computing bounds for the norm of the error in the preconditioned conjugate gradient algorithm. Numerical Algorithms v 22 (1999) pp 353-365.

  • Gaussian elimination for the solution of linear systems of equations. Handbook of Numerical Analysis, P.G. Ciarlet and J-L. Lions Eds, vol VII, North-Holland (2000) pp 3-170.

  • On the incomplete Cholesky decomposition of a class of perturbed matrices. SIAM J. of Scientific Computing, v 23 no 2 (2001) pp 419-429.

  • Numerical experiments with algebraic multilevel preconditioners. Electronic Transactions on Numerical Analysis, vol 12 (2001) pp 1-65.

  • A multilevel AINV preconditioner. Numerical Algorithms v 29 n 1-3 (2002) pp 107-129.

  • Estimates of the l2 norm of the error in the conjugate gradient algorithm. Numerical Algorithms v 40 n 2 (2005) pp 157-169.

  • Gene H. Golub 1932--2007. Numerical Algorithms, v 51 n 1 (2009), pp 1--4.

  • Estimates of the trace of the inverse of a symmetric matrix using the modified Chebyshev algorithm. Numerical Algorithms, v 51 n 3 (2009), pp 309--318.

  • On the residual norm in FOM and GMRES}, SIAM J. Matrix Anal. Appl., v 32 (2011), pp 394--411.

  • Estimates of the norm of the error in solving linear systems with FOM and GMRES}, SIAM J. Sci. Comput., v 33 (2011), pp 2686--2705.

  • The computation of isotropic vectors. Numerical Algorithms, v 60 n 2 (2012), pp 193-204.

  • The complete stagnation of GMRES for n<4. Electronic Transactions on Numerical Analysis, v 39 (2012), pp 75-101.

  • GMRES and the Arioli, Ptak and Strakos parametrization. BIT Numerical Algorithms, v 52 n 3 (2012), pp 687-702.

  • Necessary and sufficient conditions for GMRES complete and partial stagnation. Applied Numerical Mathematics, v 75 (2014), pp 100-107.

  • On the location of the Ritz values in the Arnoldi process. Electronic Transactions on Numerical Analysis, v 43 (2015), pp 188-212.

  • An optimal Q-OR Krylov subspace method for solving linear systems. Electronic Transactions on Numerical Analysis, v 47 (2017), pp 127-152.

  • The coefficients of the FOM and GMRES residual polynomials. SIAM J. Matrix Anal. Appl., v 38 n 1 (2017), pp 96-117.

  • On prescribing the convergence behavior of the conjugate gradient algorithm. Numerical Algorithms, v 84 n 4 (2020), pp 1353-1380.

  • Detection and correction of silent errors in the conjugate gradient algorithm. Numerical Algorithms, v 92 n 1 (2023), pp 869-891.



    Papers in Journals with collaborators

  • G. MEURANT & J.C. SAUT, Bifurcation and stability in chemical systems. J. Math. Anal. & Appl. v 59 n 1 (1977) pp. 69-92.

  • P. CONCUS, G.H. GOLUB & G. MEURANT, Block preconditioning for the conjugate gradient method. SIAM J. Sci. Stat. Comp., v 6, (1985) pp. 220-252.

  • P. CONCUS & G. MEURANT, On computing INV block preconditionings for the conjugate gradient method. BIT v 26 (1986) pp. 493-504.

  • Y. CHAUVET & G. MEURANT, Multitasking on the CRAY X-MP 2. in Proceedings of International workshop on modeling and performance evaluation of parallel systems, IMAG Grenoble (1984), published in the Journal of Systems and Software, v 6 n 1 & 2 (1986) pp. 17-20.

  • I.S. DUFF & G. MEURANT, The effect of ordering on preconditioned conjugate gradients. BIT v 29 (1989) pp. 635-657.

  • P. JOLY & G. MEURANT, Complex conjugate gradient methods. Numerical Algorithms v 4 (1992) pp. 379-406.

  • G. MEURANT & O. PIRONNEAU, Trends in architectures for large-scale scientific computing. Eccomas Newsletter v 2 n 1 (1994) pp. 3-5.

  • G.H. GOLUB & G. MEURANT, Matrices, moments and quadrature II: how to compute the norm of the error in iterative methods. BIT v 37 n3 (1997). pp. 687-705.

  • L.M. CARVALHO, L. GIRAUD & G. MEURANT, Local preconditioners for two-level non-overlapping domain decomposition methods. Numerical Linear Algebra with Applications, v 8 n 4 (2001) pp. 207-227.

  • G. MEURANT & Z. STRAKOS, The Lanczos and conjugate gradient algorithms in finite precision arithmetic. Acta Numerica v 15 Cambridge University Press (2006) pp. 471-542.

  • R. BOUYOULI, G. MEURANT, L. SMOCH & H. SADOK, New results on the convergence of the conjugate gradient method. Numerical Linear Algebra with Applications, v 16 n 3, (2008), pp. 223--236.

  • G. MEURANT & P. TICHY, On computing quadrature-based bounds for the A-norm of the error in conjugate gradients. Numerical Algorithms, v 62 n 2, (2012), pp. 163-191.

  • J. DUINTJER TEBBENS & G. MEURANT, Any Ritz value behavior is possible for Arnoldi and for GMRES. SIAM J. of Matrix Anal. and Appl., v 33 n 3, (2012), pp. 958-978.

  • J. DUINTJER TEBBENS & G. MEURANT, Prescribing the behavior of early terminating GMRES and Arnoldi iterations. Numerical Algorithms, v 65 n 1, (2014), pp. 69-90.

  • J. DUINTJER TEBBENS, G. MEURANT, H. SADOK & Z. STRAKOS, On investigating GMRES convergence using unitary matrices. Linear Algebra and its Applications, v 450, (2014), pp. 83-107.

  • A. SOMMARIVA & G. MEURANT, Fast variants of the Golub and Welsch algorithm for symmetric weight functions in Matlab. Numerical Algorithms, v 67 n 3 (2014), pp. 491-506..

  • G. MEURANT & J. DUINTJER TEBBENS, The role eigenvalues play in forming GMRES residual norms with non-normal matrices. Numerical Algorithm,s v 68 n 1 (2015), pp. 143-165.

  • J. DUINTJER TEBBENS & G. MEURANT, On the convergence of Q-OR and Q-MR Krylov methods for solving nonsymmetric linear systems, BIT Numerical Mathematics, v 56 n 1 (2016), pp.. 77-97.

  • M. BELLALIJ, G. MEURANT & H. SADOK, The distance of an eigenvector to a Krylov subspace and the convergence of the Arnoldi method for eigenvalue problems, Linear Algebra and its Applications, v 504 (2016); pp. 387-405.

  • K. DU, J. DUINTJER TEBBENS & G. MEURANT, Any admissible harmonic Ritz value set is possible for GMRES. Electronic Transactions on Numerical Analysis, v 47 (2017), pp. 37-56.

  • G. MEURANT & P. TICHY, Approximating the extreme Ritz values and upper bounds for the A-norm of the error in CG. Numerical Algorithms, v 82 n 3 (2019), pp.. 937-968.

  • G. MEURANT & A. SOMMARIVA, On the computation of sets of points with low Lebesgue constant on the unit disk. Journal of Computational and Applied Mathematics, v 345 (2019), pp. 388-404.

  • J. DUINTJER TEBBENS & G. MEURANT, On the residual norms, the Ritz values and the harmonic Ritz values that can be generated by restarted GMRES. Numerical Algorithms, v 84 n 4 (2020), pp. 1329-1352.

  • G. MEURANT, J. PAPEZ & P. TICHY, Accurate error estimation in CG. Numerical Algorithms, v 88 n 3 (2021), pp.. 1337-1359.

  • G. MEURANT & P. TICHY, The behaviour of the Gauss-Radau upper bound of the error norm in CG. Numerical Algorithms, v 94 n 2 (2023), pp. 847-876.

  • T. CHEN & G. MEURANT, Near-optimal convergence of the full orthogonalization method. Electronic Transactions on Numerical Analysis, v 60 (2024), pp. 421-427.

  • H. ALMUTAIRI, G. MEURANT, L. REICHEL & M. M. SPALEVIC, New error estimates for the conjugate gradient method. J. Comput. Appl. Math., v 459 (2025), Art 116357.



    Papers in Proceedings

  • G. MEURANT, B. SCHEURER & F. TERNAY, Méthodes d'éléments finis mixtes pour la résolution des équations de la diffusion en transfert radiatif. Colloque international sur les développements nouveaux dans les méthodes numériques de l'ingénieur, Versailles, May 23-27, (1977).

  • M. BONNET & G. MEURANT, Comparaison de différentes méthodes itératives de résolution des systèmes linéaires et non linéaires. in "Méthodes numériques dans les sciences de l'ingénieur", E. Absi & R. Glowinski Eds, (1979) pp. 575-584, Dunod, Paris.

  • G. MEURANT, Vector preconditioning for the conjugate gradient method on Cray 1 and CDC Cyber 205. In "Computing methods in applied sciences and engineering VI" R. Glowinski & J.L. Lions Eds North-Holland (1984) pp. 255-274.

  • R. CHERET, R. DAUTRAY, J.C. DESGRAZ, B. MERCIER, G. MEURANT, J. OVADIA & B. SITT, Topics in the numerical simulation of high temperature flows. In "Proceedings of the 9th international conference on numerical methods in fluid dynamics", Soubbarameyer & J.P. Boujot Eds, Lecture Notes in Physics n 218, Springer Verlag (1985) pp. 10-22.

  • B. MERCIER, G. MEURANT & J. TASSART, Energy conservation in radiation hydrodynamics, application to the Monte Carlo method used for photon transport in the fluid frame. In "Monte Carlo methods and applications in neutronics, photonics and statistical physics", R. Alcouffe, R. Dautray, A. Forster, G. Ledanois & B. Mercier Eds, Lecture Notes in Physics n 240, Springer Verlag (1985) pp. 116-125.

  • G. MEURANT, Incomplete domain decomposition preconditioners for the conjugate gradient method. In "Proceedings of the third SIAM conference on parallel processing for scientific computing", Los Angeles 1987, SIAM (1988).

  • G. MEURANT, Domain decomposition vs block preconditioning. In "Proceedings of the first international symposium on domain decomposition methods for partial differential equations",R. Glowinski, G.H. Golub, G. Meurant & J. Periaux Eds., SIAM (1988).

  • G. MEURANT, Using the CEA benchmark on supercomputers. In "Evaluating supercomputers" A. van der Steen Ed., Unicom, London (1988) .

  • G. MEURANT, Domain decomposition preconditioners for non symmetric problems. In "Proceedings of the second international symposium on domain decomposition methods for partial differential equations", T. Chan, R. Glowinski, J. Periaux & O. Widlund Eds, SIAM (1989).

  • G. MEURANT, Domain decomposition for partial differential equations on parallel computers. In "Vector and parallel computing" J. Dongarra, I. Duff, P. Gaffney & S. McKee Eds, Ellis Horwood (1989).

  • G. MEURANT, The conjugate gradient method on vector and parallel supercomputers. In "Computational techniques and applications", W.L. Hogarth & B.J. Noye Eds, Hemisphere Publishing Corp. (1990).

  • G. MEURANT, Numerical experiments with a domain decomposition method for parabolic equations on parallel computers. In "Proceedings of the fourth international symposium on domain decomposition methods for partial differential equations",R. Glowinski, G. Meurant, J. Periaux & O. Widlund Eds., SIAM (1991).

  • G. MEURANT, Parallel algorithms for supercomputers. In "Numerical linear algebra, digital signal processing and parallel algorithms", G. Golub & P. van Dooren Eds. Springer Verlag (1990).

  • G. MEURANT, Domain decomposition methods for solving large sparse linear systems. In "Computer algorithms for solving linear algebraic equations, the state of the art", Proceedings of the NATO Advanced Study Institute on linear systems, Castelvecchio Pascoli (Italy), E. Spedicato Ed., NATO ASI Series v 77, Springer Verlag (1991).

  • G.H. GOLUB & G. MEURANT, Matrices, moments and quadrature. In "Numerical analysis 1993", D.F. Griffiths and G.A. Watson Eds., Longman Scientific & Technical, Pitman Research Notes in Mathematics Series, v 303 (1994).

  • P. CIARLET Jr. & G. MEURANT, A class of domain decomposition preconditioners for massively parallel computers. Comtemporary Mathematics v 152, AMS (1994).

  • G. MEURANT, M. PATRON, T. PORCHER & F. ROBIN, Early experiments with the CRAY T3D at CEA. In "Proceedings of the 6th joint EPS-APS international conference on Physics Computing", R. Gruber & M. Tomassini Eds., APS (1994).

  • L. CROUZET & G. MEURANT, Solving the 3D time harmonic Maxwell equations with finite elements, Lagrange multipliers and iterative methods. In "Proceedings of the meeting 50 years of the Courant element", Jyvaskyla, Finland (1994).

  • G. MEURANT, H. JOURDREN & B. MELTZ, Large scale CFD computations at CEA. In "Proceedings of the Parallel CFD conference 2001", invited lecture at PARCFD 2001, Egmond aan Zee, The Netherlands.

  • G. MEURANT, Parallel algebraic multilevel preconditioners. In "Proceedings of the meeting in honor of the 60th birthday of Jacques Périaux", Jyvaskyla, Finland, June 2002.