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

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