  We consider the iterative solution of anisotropic radiative transfer problems
using residual minimization over suitable subspaces. We show convergence of the
resulting iteration using Hilbert space norms, which allows us to obtain
algorithms that are robust with respect to finite dimensional realizations via
Galerkin projections. We investigate in particular the behavior of the
iterative scheme for discontinuous Galerkin discretizations in the angular
variable in combination with subspaces that are derived from related diffusion
problems. The performance of the resulting schemes is investigated in numerical
examples for highly anisotropic scattering problems with heterogeneous
parameters.
