  Dynamical low-rank approximation in the Tucker tensor format of given large
time-dependent tensors and of tensor differential equations is the subject of
this paper. In particular, a discrete time integration method for
rank-constrained Tucker tensors is presented and analyzed. It extends the known
projector-splitting integrator for dynamical low-rank approximation of matrices
to Tucker tensors and is shown to inherit the same favorable properties. The
integrator is based on iteratively applying the matrix projector-splitting
integrator to tensor unfoldings but with inexact solution in a substep. It has
the property that it reconstructs time-dependent Tucker tensors of the given
rank exactly. The integrator is also shown to be robust to the presence of
small singular values in the tensor unfoldings. Numerical examples with
problems from quantum dynamics and tensor optimization methods illustrate our
theoretical results.
