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.
Marcos Raydan (Universidad Simón Bolívar)
On the computation of large-scale self-consistent-field iterationsInformations : 11:00 - 12:00 B014
The computation of the subspace spanned by the eigenvectors associated to the N lowest eigenvalues of a large symmetric matrix (or, equivalently, the projection matrix onto that subspace) is a difficult numerical linear algebra problem when the dimensions involved are very large.
These problems appear when one employs the SCF (Self-Consistent-Field) fixed-point algorithm or its variations for electronic structure calculations, which requires repeated solutions of the problem for different data, in an iterative context. The naive use of consolidated packages as Arpack does not
lead to practical solutions in large-scale cases. In this paper we combine and enhance well-known purification iterative schemes with a specialized use of Arpack (or any other eigen-package) to address these large-scale challenging problems.
Abderrahim Messaoudi (ENS, Université Mohammed VI, Rabat)
GRPIA : a new algorithm for computing interpolation polynomialsInformations : 10:00 - 11:00 B014
Le fichier pdf du résumé est disponible ici.
Fadi Dornaika (University of the Basque Country UPV/EHU)
Contribution to machine learning tools : Applications to visual data analysisInformations : 13:30 - 14:30 B014
The first part of the talk addresses some of my recent contributions to semi-supervised learning. Data driven graphs and semi-supervised learning constitute a cornerstone of many machine learning algorithms. More precisely, we have introduced a Two phases weighted Regularized Least square method which provides adaptive and informative graphs. We have also proposed inductive and flexible schemes for graph-based semi-supervised learning that provide non-linear projections. The performance of the proposed methods is studied on real image datasets including faces and objects.
The second part of the talk will briefly present some of my recent works that exploit machine learning tools for visual data analysis. These are as follows : object detection in aerial images, vision-based vehicle localization, parking lot occupancy detection, image based age estimation, assessing face attractiveness, Five Psychology Traits from videos, and Driver Drowsiness detection in videos.
Karim Kreit (Université Caddi Ayad Marrakech)
Groupe de travail approximation et analyse matricielleInformations : 14:30 - 15:00 Salle B014
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.
Achraf Badahmane (ULCO-LMPA)
The preconditioned global MINRESInformations : 11:00 - 12:00 B014
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.
Yassine Kaouane (ULCO)
An adaptive block tangential method for multi-input multi-output dynamical systems.Informations : 11:00 - 12:00 Salle B014
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.
Groupe de travail approximation et analyse matricielle du 30 juin 2017A. Messaoudi (ENS, Université Mohammed VI, Rabat)
New algoritm for computing the interpolation polynomialsInformations : 11:00 - 12:00 B014
Le résumé est diponible ici pdf
Groupe de travail approximation et analyse matricielle du 23 juin 2017Marcos Raydan (Universidad Simón Bolívar)
Constrained optimization schemes for avoiding resonance in large structuresInformations : 11:00 - 12:00 B014
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.
Groupe de travail approximation et analyse matricielle du 16 juin 2017Achraf Badahmane (ULCO)
Saddle point problemsInformations : 14:30 - 15:30 B014
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
Groupe de travail approximation et analyse matricielle du 2 juin 2017Yassine Kaouane (LMPA, ULCO)
Adaptive tangential Computational Krylov subspaces methods for model reduction in large-scale dynamical systemsInformations : 14:30 - 15:30 B014, Mi-voix
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.