Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement

The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of refinement to enhance methods sparse based approximate factorizations. In doing so, we first develop a new error analysis LU- and GMRES-based under general model factorization that accounts approximation typically used modern solvers, such as low-rank approximations relaxed pivoting strategies. then provide detailed performance both execution time memory consumption different algorithms, selected set variants Our study uses multifrontal solver MUMPS, which exploit block static pivoting. evaluate algorithms large, problems coming from variety real-life industrial applications showing combined with lead considerable reductions consumption.