  Recent development on mixed precision techniques has largely enhanced the
performance of various linear algebra solvers, one of which being the least
squares problem $\min_{x}\lVert b-Ax\rVert_{2}$. By transforming the least
squares problem into an augmented linear system, mixed precision techniques are
capable of refining the lower precision solution to the working precision. In
this paper, we propose mixed precision iterative refinement algorithms for two
variants of the least squares problem -- the least squares problem with linear
equality constraints (LSE) and the generalized least squares problem (GLS).
Both classical and GMRES-based iterative refinement can be applied to augmented
systems of these two problems to improve the accuracy of the solution. For
reasonably well-conditioned problems our algorithms reduce the execution time
by a factor of 40% in average compared to the fixed precision ones from LAPACK
on the x86-64 architecture.
