With Graphics Processing Units (GPUs) capable of teraflop performance double digit speedups over single core execution are possible. An alternative application of GPU acceleration is quality up: if we can afford to wait the same amount of time as on a single core, then how much more accurately can we compute the same result? A multiple double is an unevaluated sum of doubles and multiple double arithmetic exploits the optimized hardware for floating-point arithmetic, with predictable overhead and simple memory management.

The talk will present experiences with software package QDlib (Hida, Li, Bailey, 2001) and the more recent CAMPARY software (Joldes, Muller, Popescu, Tucker, 2016) on NVIDIA GPUs, in particular the P100, V100, and RTX 2080. Code to evaluate and differentiate polynomials at power series and to accelerated the blocked Householder QR in multiple double precision is used in the software PHCpack, publicly available at github, and released under the GNU GPL v3.0 license.