PRIMME: PReconditioned Iterative MultiMethod Eigensolver-Methods and Software Description

This article describes the PRIMME software package for solving large, sparse Hermitian standard eigenvalue problems. The difficulty and importance of these problems have increased over the years, necessitating the use of preconditioning and near optimally converging iterative methods. However, the complexity of tuning or even using such methods has kept them outside the reach of many users. Responding to this problem, we have developed PRIMME, a comprehensive package that brings state-of-the-art methods from bleeding edge to production, with the best possible robustness, efficiency, and a flexible, yet highly usable interface that requires minimal or no tuning. We describe (1) the PRIMME multimethod framework that implements a variety of algorithms, including the near optimal methods GD+k and JDQMR; (2) a host of algorithmic innovations and implementation techniques that endow the software with its robustness and efficiency; (3) a multilayer interface that captures our experience and addresses the needs of both expert and end users.