  Computing effective eigenvalues for neutron transport often requires a fine
numerical resolution. The main challenge of such computations is the high
memory effort of classical solvers, which limits the accuracy of chosen
discretizations. In this work, we derive a method for the computation of
effective eigenvalues when the underlying solution has a low-rank structure.
This is accomplished by utilizing dynamical low-rank approximation (DLRA),
which is an efficient strategy to derive time evolution equations for low-rank
solution representations. The main idea is to interpret the iterates of the
classical inverse power iteration as pseudo-time steps and apply the DLRA
concepts in this framework. In our numerical experiment, we demonstrate that
our method significantly reduces memory requirements while achieving the
desired accuracy. Analytic investigations show that the proposed iteration
scheme inherits the convergence speed of the inverse power iteration, at least
for a simplified setting.
