A fast and robust mixed-precision solver for the solution of sparse symmetric linear systems

Abstract

On many current and emerging computing architectures, single-precision calculations are at least twice as fast as double-precision calculations. In addition, the use of single precision may reduce pressure on memory bandwidth. The penalty for using single precision for the solution of linear systems is a potential loss of accuracy in the computed solutions. For sparse linear systems, the use of mixed precision in which double-precision iterative methods are preconditioned by a single-precision factorization can enable the recovery of high-precision solutions more quickly and use less memory than a sparse direct solver run using double-precision arithmetic. In this article, we consider the use of single precision within direct solvers for sparse symmetric linear systems, exploiting both the reduction in memory requirements and the performance gains. We develop a practical algorithm to apply a mixed-precision approach and suggest parameters and techniques to minimize the number of solves required by the iterative recovery process. These experiments provide the basis for our new code HSL_MA79—a fast, robust, mixed-precision sparse symmetric solver that is included in the mathematical software library HSL. Numerical results for a wide range of problems from practical applications are presented.