The Eigenvalues Slicing Library (EVSL): Algorithms, Implementation, and Software

Abstract

This paper describes a software package called EVSL (for eigenvalues slicing library) for solving large sparse real symmetric standard and generalized eigenvalue problems. As its name indicates, the package exploits spectrum slicing, a strategy that consists of dividing the spectrum into a number of subintervals and extracting eigenpairs from each subinterval independently. In order to enable such a strategy, the methods in EVSL utilize a quick calculation of the spectral density of a given matrix (or matrix pair). What distinguishes EVSL from other available packages is that EVSL relies entirely on filtering techniques. Both polynomial and rational classes of filtering are implemented and are coupled with Krylov subspace methods as well as subspace iteration. On the implementations, the package offers interfaces for various scenarios including matrix-free approaches, whereby user-specific functions can be supplied to perform matrix-vector operations or solve linear systems. The paper describes the algorithms in EVSL, provides details on their implementations, and discusses performance issues for the various methods and on various computing platforms.