L.M.P.A
Laboratoire de Mathématiques Pures et Appliquées
Joseph Liouville

Séminaire et groupe de travail d’Approximation et Analyse matricielle

Le séminaire et groupe de travail d’algèbre réunit les membres de l’équipe Approximation (et toutes personnes intéressées). Responsable : Khalide Jbilou.

Prochain évènement

Séminaire et groupe de travail d’Approximation et Analyse matricielle du 25 juin

Stefano Pozza (Charles University, Prague)

Let A(t) be a time-dependent matrix with t in an interval. The time-ordered exponential of A(t) is defined as the unique solution U(t) of the system of coupled linear differential equations A(t)U(t)=d/dt U(t) with initial condition U(0)=I. In the general case (when A does not commute with itself at all times), the ordered exponential has no known explicit form in terms of A. The problem of evaluating U(t) is a central question in the field of system dynamics, in particular in quantum physics where A is the quantum Hamiltonian.
Until now, few methods have been proposed to approximate the ordered exponential, but a satisfactory answer to this problem is still missing. In 2015, P.-L. Giscard proposed a method to obtain ordered exponentials using graph theory and necessitating only the entries A(t) to be bounded functions of time. While this approach provides exact solutions and is always convergent, it suffers from computational drawbacks. The talk will describe a model-reduction strategy that solves such computational issue by a Lanczos-like algorithm, giving a converging and computable (in term of complexity) strategy for getting U(t). Such a technique is based on the connections between the Lanczos-like algorithm and the moment problem, graph approximations, and continued fractions.

Informations : 13:30 - 14:30 C115

Évènements passés


  • Séminaire et groupe de travail d’Approximation et Analyse matricielle du 16 mars 2018

    Achraf Badahmane (ULCO-LMPA)

    In this talk, we propose the preconditioned global MINRES as a new strategy to solve problems $AX=B$ with several right-hand sides.
    The preconditioner is obtained by replacing the block (2,2) by another block of the matrix A.
    We apply the global MINRES method for this problem with several right hand sides and we give new convergence results and analyze the eigenvalue-distribution and the eigenvectors of the preconditioner.
    Finally, numerical results show that our preconditioned global MINRES method, is very efficient for solving problem with several right hand sides.

    Informations : 11:00 - 12:00 B014

  • Séminaire et groupe de travail d’Approximation et Analyse matricielle du 9 février 2018

    Yassine Kaouane (ULCO)

    We present a new approach for model order reduction in large-scale dynamical systems, with multiple inputs and multiple outputs (MIMO). This approach will be named : Adaptive Block Tangential Arnoldi Algorithm (ABTAA) and is based on interpolation via block tangential Krylov subspaces requiring the selection of shifts and tangent directions via an adaptive procedure. We give some algebraic properties and present some numerical examples to show the effectiveness of the proposed method.

    Informations : 11:00 - 12:00 Salle B014

  • Séminaire et groupe de travail d’Approximation et Analyse matricielle du 30 juin 2017

    A. Messaoudi (ENS, Université Mohammed VI, Rabat)

    Le résumé est diponible ici pdf

    Informations : 11:00 - 12:00 B014

  • Séminaire et groupe de travail d’Approximation et Analyse matricielle du 23 juin 2017

    Marcos Raydan (Universidad Simón Bolívar)

    The Quadratic Finite Element Model Updating Problem (QFEMUP) concerns
    with updating a symmetric second-order finite element model so that it
    remains symmetric and the updated model reproduces a given set of
    desired eigenvalues and eigenvectors by replacing the corresponding
    ones from the original model. Taking advantage of the special
    structure of the constraint set, it is first shown that the QFEMUP can
    be formulated as a suitable constrained nonlinear programming
    problem. Using this formulation, we present and analyze two different
    methods based on successive optimizations. To avoid that spurious
    modes (eigenvectors) appear in the frequency range of interest
    (eigenvalues) after the model has been updated, additional constraints
    based on a quadratic Rayleigh quotient are dynamically included in the
    constraint set. The results of our numerical experiments on
    illustrative problems show that the algorithms work well in practice.

    Informations : 11:00 - 12:00 B014

  • Séminaire et groupe de travail d’Approximation et Analyse matricielle du 16 juin 2017

    Achraf Badahmane (ULCO)

    In some applications, we have to solve large linear saddle
    point problems with multiple right-hand sides. Instead of applying a
    standard iterative process to the solution of each saddle point
    problem indepentely, it’s more efficient to apply a global process. We
    use different techniques of preconditioning ( Diagonal preconditioner,
    Triangular preconditioner, P0 preconditioner ,.. ) to improve spectral
    proprieties of the saddle point matrix and to accelerate the
    convergence

    Informations : 14:30 - 15:30 B014

  • Séminaire et groupe de travail d’Approximation et Analyse matricielle du 2 juin 2017

    Yassine Kaouane (LMPA, ULCO)

    In this talk, we present two new approaches for model order reduction
    problem, with multiple inputs and multiple outputs (MIMO). The
    Adaptive Global Tangentiel Arlondi Algorithms (AGTAA), and the
    Adaptive Global Tangentiel Lanczos Algorithms (AGTLA).These methods
    are based on a generalization of the global Arnoldi and the global
    Laczos algorithms. The selection of the shifts and the tangent
    directions is done with an adaptive procedure. We give some algebraic
    properties for the global case. Finally, some numerical examples are
    presented to show the effectiveness of the proposed algorithms.

    Key words : Global, Arnoldi, Lanczos, Model reduction, Tangential directions.

    Informations : 14:30 - 15:30 B014, Mi-voix

  • Séminaire et groupe de travail d’Approximation et Analyse matricielle du 12 mai 2017

    Hassane Sadok (ULCO)

    Krylov subspace methods are widely used for the iterative solution of
    a large variety of linear systems of equations with one or several
    right hand sides or for solving nonsymmetric eigenvalue problems. The
    solution of linear systems of equations with several right-hand sides
    is considered. Approximate solutions are conveniently computed by
    block GMRES methods. We describe and study three variants of block
    GMRES. These methods are based on three implementations of the block
    Arnoldi method, which differ in their choice of inner product.. The
    Block GMRES is classically implemented by first applying the Arnoldi
    iteration as a block orthogonalization process to create a basis of
    the block Krylov space generated by the matrix of the system from the
    initial residual. Next, the method is solving a block least-squares
    problem, which is equivalent to solving several least squares problems
    implying the same Hessenberg matrix. These laters are usually solved
    by using a block updating procedure for the QR decomposition of the
    Hessenberg matrix based on Givens rotations. A more effective
    alternative was given by M. H. Gutknecht and T. Schmelzer which uses
    the Householder reflectors. We propose a new and simple implementation
    of the block GMRES algorithm, based on a generalization of Ayachour’s
    method given for the GMRES with a single right-hand side. Several
    numerical experiments are provided to illustrate the performance of
    the new implementation.

    Informations : 13:30 - 14:30 B014
Autres évènements passés : 0 | 10

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