  Various approaches to iterative refinement (IR) for least-squares problems
have been proposed in the literature and it may not be clear which approach is
suitable for a given problem. We consider three approaches to IR for
least-squares problems when two precisions are used and review their
theoretical guarantees, known shortcomings and when the method can be expected
to recognize that the correct solution has been found, and extend uniform
precision analysis for an IR approach based on the semi-normal equations to the
two-precision case. We focus on the situation where it is desired to refine the
solution to the working precision level. It is shown that the IR methods
exhibit different sensitivities to the conditioning of the problem and the size
of the least-squares residual, which should be taken into account when choosing
the IR approach. We also discuss a new approach that is based on solving
multiple least-squares problems.
