Leveraging accelerators in the multiple implicitly restarted Arnoldi method with nested subspaces

Abstract

We present a parallel, hybrid solver to compute a set of eigenpairs of large, sparse, non-symmetric matrices. The implicitly restarted Arnoldi method (IRAM) is a method to compute a set of eigenpairs of large sparse general matrices based on Krylov subspace techniques. The subspace size has an important impact on the performances, however, it is selected empirically in advance in this method. MIRAMns, a variant of IRAM, generates multiple subspaces in a nested fashion in order to dynamically pick the best one inside each restart cycle. Parallelism and performance are critical for the overall success of this method, thus, accelerators should to be considered. We show how MIRAMns benefits from that, present a general hybrid algorithm, and a GPU implementation. Our experiments show interesting speedup and lead to new suggestions to improve MIRAMns.