Algebraic Error Analysis for Mixed-Precision Multigrid Solvers

This paper establishes the first theoretical framework for analyzing the rounding-error effects on multigrid methods using mixed-precision iterative-refinement solvers. Additionally, it introduces the notion of progressive precision for multigrid solvers where each level of the multigrid hierarchy uses three different precisions that each increase with the fineness of the level. The precisions increase at different rates, thereby ensuring that the bulk of the computation uses the lowest possible precision.