A thick-restart lanczos algorithm with polynomial filtering for hermitian eigenvalue problems

Ruipeng Li, Yuanzhe Xi, Eugene Vecharynski, Chao Yang, Yousef Saad

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25 Scopus citations

Abstract

Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for tackling this problem by combining a thick- restart version of the Lanczos algorithm with deation (\locking") and a new type of polynomial filter obtained from a least-squares technique. The resulting algorithm can be utilized in a \spectrum- slicing" approach whereby a very large number of eigenvalues and associated eigenvectors of the matrix are computed by extracting eigenpairs located in different subintervals independently from one another.

Original languageEnglish (US)
Pages (from-to)A2512-A2534
JournalSIAM Journal on Scientific Computing
Volume38
Issue number4
DOIs
StatePublished - 2016

Keywords

  • Deation
  • Interior eigenvalue problems
  • Lanczos algorithm
  • Polynomial filtering
  • Spectrum slicing
  • Thick-restart

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