1 citations · 1 across the 3 of their papers we have counts for
4 papers
A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds
Marie Billaud-Friess, Antonio Falcó, Anthony Nouy
In this paper, we propose a new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of the set of fixed rank matrices. We first introdu…
Stochastic methods for solving high-dimensional partial differential equations
Marie Billaud-Friess, Arthur Macherey, Anthony Nouy +1
We propose algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, wi…
Principal bundle structure of matrix manifolds
Marie Billaud-Friess, Antonio Falco, Anthony Nouy
In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the Grassmann manifold $\mathbb…
A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems
Marie Billaud-Friess, Anthony Nouy, Olivier Zahm
In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation forma…