Groupe de travail approximation et analyse matricielle

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

Evénements passés

• Groupe de travail approximation et analyse matricielle du 10 avril

  Karim Kreit (Université Caddi Ayad Marrakech)

  
  

  Groupe de travail approximation et analyse matricielle

  The total variation model has been introduced in image processing since $1992$ by Rudin, Osher and Fatemi (ROF). The (ROF) model eliminates noise from images and preserve the edges by solving a minimization problem related to a total variation energy.
  In this talk, we consider the problem of image restoration with total variation regularization. We transform the problem to a nonlinear constrained optimization in the dual form. We apply the conditional gradient (Frank-Wolfe) method to the dual total variation regularization, and we drive a new method for denoising image. The convergence of this method is proved. Finally we illustrate the effectiveness of our proposed method by some numerical examples.

  Informations : 14:30 - 15:00 Salle B014

• Groupe de travail approximation et analyse matricielle du 16 mars

  Achraf Badahmane (ULCO-LMPA)

  
  

  The preconditioned global MINRES

  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

• Groupe de travail approximation et analyse matricielle du 9 février

  Yassine Kaouane (ULCO)

  
  

  An adaptive block tangential method for multi-input multi-output dynamical systems.

  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

• Groupe de travail approximation et analyse matricielle du 30 juin 2017

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

  
  

  New algoritm for computing the interpolation polynomials

  Le résumé est diponible ici pdf

  Informations : 11:00 - 12:00 B014

• Groupe de travail approximation et analyse matricielle du 23 juin 2017

  Marcos Raydan (Universidad Simón Bolívar)

  
  

  Constrained optimization schemes for avoiding resonance in large structures

  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

• Groupe de travail approximation et analyse matricielle du 16 juin 2017

  Achraf Badahmane (ULCO)

  
  

  Saddle point problems

  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

• Groupe de travail approximation et analyse matricielle du 2 juin 2017

  Yassine Kaouane (LMPA, ULCO)

  
  

  Adaptive tangential Computational Krylov subspaces methods for model reduction in large-scale dynamical systems

  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

• Groupe de travail approximation et analyse matricielle du 12 mai 2017

  Hassane Sadok (ULCO)

  
  

  Convergence properties and implementations of Block Krylov subspaces methods

  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