A rank-adaptive robust integrator for dynamical low-rank approximation

A rank-adaptive integrator for the dynamical low-rank approximation of matrix and tensor differential equations is presented. The fixed-rank recently proposed by two authors extended to allow an adaptive choice rank, using subspaces that are generated itself. first updates evolving bases then does a Galerkin step in subspace both new old bases, which followed rank truncation given tolerance. It shown retains exactness, robustness symmetry-preserving properties previously integrator. Beyond that, up tolerance, preserves norm when equation does, it energy Schrödinger Hamiltonian systems, monotonic decrease functional gradient flows. Numerical experiments illustrate behaviour