  We propose and analyse a numerical integrator that computes a low-rank
approximation to large time-dependent matrices that are either given explicitly
via their increments or are the unknown solution to a matrix differential
equation. Furthermore, the integrator is extended to the approximation of
time-dependent tensors by Tucker tensors of fixed multilinear rank. The
proposed low-rank integrator is different from the known projector-splitting
integrator for dynamical low-rank approximation, but it retains the important
robustness to small singular values that has so far been known only for the
projector-splitting integrator. The new integrator also offers some potential
advantages over the projector-splitting integrator: It avoids the backward time
integration substep of the projector-splitting integrator, which is a
potentially unstable substep for dissipative problems. It offers more
parallelism, and it preserves symmetry or anti-symmetry of the matrix or tensor
when the differential equation does. Numerical experiments illustrate the
behaviour of the proposed integrator.
