A projector-splitting integrator for dynamical low-rank approximation

Understand

The dynamical low-rank approximation of time-dependent matrices is a low-rank factorization updating technique.

• It leads to differential equations for factors of the matrices, which need to be solved numerically.
• We propose and analyze a fully ex- plicit, computationally inexpensive integrator that is based on splitting the orthogonal projector onto the tangent space of the low-rank manifold.
• As is shown by theory and illustrated by numerical experiments, the integrator enjoys robustness properties that are not shared by any standard numerical integrator.