Efficient estimation of eigenvalue counts in an interval

Edoardo Di Napoli, Eric Polizzi, Yousef Saad

Research output: Contribution to journalArticlepeer-review

58 Scopus citations

Abstract

Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is an important problem in certain applications, and it is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often, an exact count is not necessary, and methods based on stochastic estimates can be utilized to yield rough approximations. This paper examines a number of techniques tailored to this specific task. It reviews standard approaches and explores new ones based on polynomial and rational approximation filtering combined with a stochastic procedure. We also discuss how the latter method is particularly well-suited for the FEAST eigensolver.

Original languageEnglish (US)
Pages (from-to)674-692
Number of pages19
JournalNumerical Linear Algebra with Applications
Volume23
Issue number4
DOIs
StatePublished - Aug 1 2016

Bibliographical note

Publisher Copyright:
Copyright © 2016 John Wiley & Sons, Ltd.

Keywords

  • Chebyshev polynomials
  • FEAST
  • eigenproblem resolvent
  • eigenvalue count
  • stochastic trace estimate
  • subspace projector

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