The Eigenvalues Slicing Library (EVSL): Algorithms, implementation, and software

Ruipeng Li, Yuanzhe Xi, Lucas Erlandson, Yousef Saad

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)C393-C415
JournalSIAM Journal on Scientific Computing
Issue number4
StatePublished - 2019

Bibliographical note

Funding Information:
∗Submitted to the journal’s Software and High-Performance Computing section February 14, 2018; accepted for publication (in revised form) April 12, 2019; published electronically August 13, 2019. The U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes. Copyright is owned by SIAM to the extent not limited by these rights. Funding: The work of the first author was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 (LLNL-JRNL-746200). The work of the fourth author was partially supported by the Scientific Discovery through Advanced Computing (SciDAC) program funded by U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences DE-SC0008877, in part (theory) by NSF under grant CCF-1505970, and by the Minnesota Supercomputer Institute.

Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics


  • Krylov subspace methods
  • Parallel computing
  • Polynomial filtering
  • Rational filtering
  • Spectral density
  • Spectrum slicing


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