Gérard Meurant



Preprints

  • Convergence of the Lanczos algorithm in presence of close eigenvalues: A numerical study. (2010). [download]

  • A parallel Lanczos method for solving symmetric positive definite linear systems. (2010). [download]

  • Prescribing the error in GMRES. (2011). [download]

  • (with A. SOMMARIVA), Fast variants of the Golub and Welsch algorithm for symmetric weight functions in Matlab, accepted in Numerical Algorithms, (2014). [download]

  • On the location of the Ritz values in the Arnoldi process, submitted, (2013). [download]

  • (with S. DUMINIL and H. SADOK), A vector extrapolation method for acceleration of multigrid iterations for linear and nonlinear problems. Submitted (2014).

  • (with J. DUINTJER TEBBENS), On the admissible convergence curves for restarted GMRES. submitted, (2014). [download]

    Papers in Journals

  • 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, v 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. [download]

  • 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. [download]

  • 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. [download]

  • 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. [download]

  • 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. [download]

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

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

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

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

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

  • 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. [download]

  • On the residual norm in FOM and GMRES. SIAM J. of Matrix Anal. and Appl., v 32 n 2, (2011), pp 394-411. [download]

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

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

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

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

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

    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. [download]

  • 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. [download]

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

  • 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. [download]

  • 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. [download]

  • 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. [download]

  • 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. [download]

  • 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. [download]

  • 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. [download]

  • 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. [download]

  • 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. [download]

  • G. MEURANT & J. DUINTJER TEBBENS, The role eigenvalues play in forming GMRES residual norms with non-normal matrices, Numerical Algorithms, online first July 2014 . [download]

    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). Reprinted in "Milestones in matrix computations, the selected works of Gene H. Golub with commentaries" R.H. Chan, C. Greif & D.P. O'Leary Eds, Oxford University Press (2007). [download]

  • 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), Lecture Notes in Pure and Appl. Math., 164, Dekker, (1994). [download]

  • G. MEURANT, H. JOURDREN & B. MELTZ, Large scale CFD computations at CEA. Invited lecture at PARCFD 2001, Egmond aan Zee, The Netherlands, In "Parallel Computational Fluid Dynamics- Practice and Theory", P. Wilders, A. Ecer, J. Periaux, N. Satofuka, (Eds.), Elsevier (2002). [download]

  • G. MEURANT, Parallel algebraic multilevel preconditioners. In Proceedings of the meeting in honor of the 60th birthday of Jacques Périaux, Jyvaskyla, Finland, June 2002, "Numerical Methods For Scientific Computing, Variational Problems and Applications" Y. Kuznetsov, P. Neittanmaki & O. Pironneau Eds. CIMNE, Barcelona (2003). [download]

    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).