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 20 juin

Marilena Mitrouli (Université d'Athènes)

In the regularized linear regression models the appropriate choice of the tuning parameter plays a dominant role in the selection of the correct model. Most statistical methods employ the tool of the generalized cross-validation (GCV) for the selection of values of this parameter. In this work, we utilize extrapolation estimates for the GCV function whose minimizers can lead to the determination of the tuning parameter. The selection of an efficient estimate depends on an appropriately defined index of proximity. Bounds and specific values are derived for this index and a thorough study proves that the proposed one-term estimate suits perfectly to statistical models with high correlated variables. This is confirmed through simulation tests for several datasets.

Informations : 11:00 - 12:00 B014

• #### Séminaire et groupe de travail d’Approximation et Analyse matricielle du 14 juin

By using a recursive method for computing a left inverse of a Krylov matrix we derive a general algorithm for the subspaces Krylov methods. This technique allows us to give all the parameters of the algorithms from the Krylov vectors. In particulier we give the condition of the existence of the algorithms based on these vectors.

Informations : 11:00 - 12:00 B014

• #### Séminaire et groupe de travail d’Approximation et Analyse matricielle du 14 juin

Abderrahim Messaoudi (Université Mohammed V - Maroc)

Recently Messaoudi et al. presented a new algorithm for computing the Hermite interpolation algorithm, for a general case, called Generalized Recursive Polynomial Interpolation Algorithm (GRPIA). In this work we will give a new formulation of the Lagrange twovariate polynomial interpolation, a result of the existence and the uniqueness of this polynomial will be given. We will show that this polynomial can be expressed as a Schur complement . So using the Sylvester’s identity, we will give a new algorithm for computing this polynomial. Some properties of this algorithm will also be discussed and a generalization of this algorithm will be proposed for the Lagrange multivariate-interpolation polynomial.

Informations : 10:00 - 11:00 B014

• #### Séminaire et groupe de travail d’Approximation et Analyse matricielle du 7 septembre 2018

Le pdf du résumé est disponible ici.

Informations : 11:00 - 12:00

• #### Séminaire et groupe de travail d’Approximation et Analyse matricielle du 15 juin 2018

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.

Informations : 11:00 - 12:00 B014

• #### Séminaire et groupe de travail d’Approximation et Analyse matricielle du 15 juin 2018

Abderrahim Messaoudi (ENS, Université Mohammed VI, Rabat)

Le fichier pdf du résumé est disponible ici.

Informations : 10:00 - 11:00 B014

• #### Séminaire et groupe de travail d’Approximation et Analyse matricielle du 14 juin 2018

Fadi Dornaika (University of the Basque Country UPV/EHU)

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.

Informations : 13:30 - 14:30 B014

• #### Séminaire et groupe de travail d’Approximation et Analyse matricielle du 10 avril 2018

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.