Compressed basis GMRES on high-performance graphics processing units

Krylov methods provide a fast and highly parallel numerical tool for the iterative solution of many large-scale sparse linear systems. To large extent, performance practical realizations these is constrained by communication bandwidth in current computer architectures, motivating investigation sophisticated techniques to avoid, reduce, and/or hide message-passing costs (in distributed platforms) memory accesses all architectures). This article leverages Ginkgo’s accessor order integrate communication-reduction strategy into (Krylov) GMRES solver that decouples storage format (i.e., data representation memory) orthogonal basis from arithmetic precision employed during operations with basis. Given execution time largely determined accesses, cost datatype transforms can be mostly hidden, resulting acceleration step via decrease volume bits being retrieved memory. Together special properties orthonormal (whose elements are bounded 1), this paves road toward aggressive customization format, which includes some floating-point as well fixed-point formats mild impact on convergence process. We develop high-performance implementation “compressed GMRES” Ginkgo algebra library using set test problems SuiteSparse Matrix Collection. demonstrate robustness advantages modern NVIDIA V100 graphics processing unit (GPU) up 50% over standard stores IEEE double-precision.