  This article studies a combination of the two state-of-the-art algorithms for
the exact solution of linear programs (LPs) over the rational numbers, i.e.,
without any roundoff errors or numerical tolerances. By integrating the method
of precision boosting inside an LP iterative refinement loop, the combined
algorithm is able to leverage the strengths of both methods: the speed of LP
iterative refinement, in particular in the majority of cases when a
double-precision floating-point solver is able to compute approximate solutions
with small errors, and the robustness of precision boosting whenever extended
levels of precision become necessary. We compare the practical performance of
the resulting algorithm with both puremethods on a large set of LPs and
mixed-integer programs (MIPs). The results show that the combined algorithm
solves more instances than a pure LP iterative refinement approach, while being
faster than pure precision boosting. When embedded in an exact branch-and-cut
framework for MIPs, the combined algorithm is able to reduce the number of
failed calls to the exact LP solver to zero, while maintaining the speed of the
pure LP iterative refinement approach.
