High-Performance Solvers for Dense Hermitian Eigenproblems

Abstract

We introduce a new collection of solvers---subsequently called EleMRRR---for large-scale dense Hermitian eigenproblems. EleMRRR solves various types of problems: generalized, standard, and tridiagonal eigenproblems. Among these, the last is of particular importance as it is a solver in its own right, as well as the computational kernel for the first two; we present a fast and scalable tridiagonal solver based on the algorithm of multiple relatively robust representations---referred to as PMRRR. Like the other EleMRRR solvers, PMRRR is part of the freely available Elemental library, and is designed to fully support both message-passing and multithreading parallelism. As a result, the solvers are equally effective in message-passing environments with and without multithreading. We conducted a thorough performance study of EleMRRR and ScaLAPACK's solvers on two supercomputers. Such a study, performed with up to $8{,}192$ cores, provides precise guidelines for assembling the fastest solver within the ScaLAPACK framework; it also indicates that EleMRRR outperforms even the fastest solvers built from ScaLAPACK's components.