Numerical multi-group flux-limited diffusion problems are found in a wide variety of contexts in many fields. One common aspect of these problems are the large linear systems that arise from the implicit finite-difference techniques that are used to solve the underlying integro-PDEs that describe the flow of radiation. These problems define an important class of linear systems worthy of further study. In order to lay the groundwork for parallel approaches to solving these systems we investigate the efficiency of a number of combinations of parallelizable preconditioners and Krylov subspace methods as applied to a series of test problems with one spatial and one spectral dimension. These test problems are designed to span the range of physical conditions that one would typically encounter in in a radiation transport simulation. In turn these test problems produce linear systems which span the range of possible properties for these systems. We describe the results found for several sparse-approximate-inverse preconditioners when applied to these problems. We also discuss the effects of row scaling and symmetric scaling on these methods. Finally, we offer some suggestions for further areas of investigation.