A projector-splitting integrator for dynamical low-rank approximation (Q2450891)

This paper considers how low rank approximations of time-dependent matrices, which are either given explicitly or are solutions of differential equations, can be found efficiently. This can be done by finding an approximation of fixed rank such that the norm of the difference is minimised over all matrices tangent to the approximation on the manifold of matrices of that rank. The authors develop an explicit scheme that is well conditioned based on the splitting of projector on the tangent space of the low rank manifold at the given position. Higher-order schemes can be constructed based on symmetric compositions, and some numerical comparisons illustrate the efficacy of the approach.