  Highly precise numerical solutions to the radiative transfer equation with
polarization present a special challenge. Here, we establish a precise
numerical solution to the radiative transfer equation with combined Rayleigh
and isotropic scattering in a 1D-slab medium with simple polarization. The 2-
Stokes vector solution for the fully discretized radiative transfer equation in
space and direction derives from the method of doubling and adding enhanced
through convergence acceleration. Updates to benchmark solutions found in the
literature to 7 places for reflectance and transmittance as well as for angular
flux follow. Finally, we conclude with the numerical solution in a partially
randomly absorbing heterogeneous medium.
