Low-rank tensor representations can provide highly compressed approximations of
functions. These concepts, which essentially amount to generalizations of classical …

Deterministic models for radiation transport describe the density of radiation particles
moving through a background material. In radiation therapy applications, the phase space of …

In this chapter we present numerical methods for low-rank matrix and tensor problems that
explicitly make use of the geometry of rank constrained matrix and tensor spaces. We focus …

The dynamical low-rank approximation (DLRA) is used to treat high-dimensional problems
that arise in such diverse fields as kinetic transport and uncertainty quantification. Even …

Dynamical low-rank integrators for matrix differential equations recently attracted a lot of
attention and have proven to be very efficient in various applications. In this paper, we …

Dynamical low-rank algorithms are a class of numerical methods that compute low-rank
approximations of dynamical systems. This is accomplished by projecting the dynamics onto …

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 …

Abstract Fractional Ginzburg-Landau equations as generalizations of the classical one have
been used to describe various physical phenomena. In this paper, we propose a numerical …

The existence and uniqueness of weak solutions to dynamical low-rank evolution problems
for parabolic partial differential equations in two spatial dimensions is shown, covering also …

A numerical integrator is presented that computes a symmetric or skew-symmetric low-rank
approximation to large symmetric or skew-symmetric time-dependent matrices that are either …