Dynamical low-rank approximation: applications and numerical experiments

Dynamical low-rank approximation is a differential-equation-based approach to efficiently compute low-rank approximations to time-dependent large data matrices or to solutions of large matrix differential equations. We illustrate its use in the following application areas: as an updating procedure in latent semantic indexing for information retrieval, in the compression of series of images, and in the solution of time-dependent partial differential equations, specifically on a blow-up problem of a reaction-diffusion equation in two and three spatial dimensions. In 3D and higher dimensions, space discretization yields a tensor differential equation whose solution is approximated by low-rank tensors, effectively solving a system of discretized partial differential equations in one spatial dimension.