Évènements du mardi Juin 2019
Journées (Calais)Informations : 24/06/2019 00:00 - 27/06/2019 00:00 Calais
Site des journées : https://sites.google.com/view/nlepdecalais062019/home
Stefano Pozza (Charles University, Prague)
Informations : 13:30 - 14:30 C106
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.
Lothar Reichel (Kent State University - USA)
Informations : 14:30 - 15:30 C106
Bregman-type iterative methods have attracted considerable attention
in recent years due to their ease of implementation and the high quality of the
computed solutions they deliver. However, these iterative methods may require a
large number of iterations and this reduces their attractiveness. This talk
describes a linearized Bregman algorithm defined by projecting the problem to
be solved into an appropriately chosen low-dimensional Krylov subspace. The
projection reduces both the number of iterations and the computational effort
required for each iteration. A variant of this solution method, in which
nonnegativity of each computed iterate is imposed, also is described. The talk
presents joint work with A. Buccini and M. Pasha.