5 papers · 1 filter
Sketch low-rank dynamics: orthogonal vs. oblique projections
Benjamin Carrel, Laura Grigori
We study how sketching techniques from randomized numerical linear algebra can be incorporated into the dynamical low-rank approximation (DLRA) of large-scale matrix differential e…
Interpolatory Dynamical Low-Rank Approximation: Theoretical Foundations and Algorithms
Benjamin Carrel, Daniel Kressner, Hei Yin Lam +1
Dynamical low-rank approximation (DLRA) is a widely used paradigm for solving large-scale matrix differential equations, as they arise, for example, from the discretization of time…
Randomized methods for dynamical low-rank approximation
Benjamin Carrel
We introduce novel dynamical low-rank methods for solving large-scale matrix differential equations, motivated by algorithms from randomized numerical linear algebra. In terms of p…
Projected exponential methods for stiff dynamical low-rank approximation problems
Benjamin Carrel, Bart Vandereycken
The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of…
Low-rank Parareal: a low-rank parallel-in-time integrator
Benjamin Carrel, Martin J. Gander, Bart Vandereycken
In this work, the Parareal algorithm is applied to evolution problems that admit good low-rank approximations and for which the dynamical low-rank approximation (DLRA) can be used…