Geometric algorithms for rank-constrained matrices and tensors (Public lecture by Bart Vandereycken, Unige)

22.09.2017 09:00 – 10:00

When data in scientific computing and machine learning is structured, it is usually advisable to exploit this structure as much as possible in theoretical analyses and numerical algorithms. I will illustrate this with the example of low-rank matrices and tensors, that have the structure of a differentiable manifold. After a very brief introduction on low-rank tensors and their use in high-dimensional problems, I will explain how a time-varying tensor can be dynamically approximated directly in low-rank format. This will result in a set of ordinary differential equations that need to be integrated numerically. Unfortunately, when treated naively, these equations are very difficult to solve. However, I will explain that a more geometric approach for the derivation of the numerical methods leads to algorithms that are provable superior to their naive counterparts.

Lieu

Bâtiment: Uni Mail

salle R040

entrée libre