A symmetric structure-preserving ΓQR algorithm for linear response eigenvalue problems

Tiexiang Li, Ren Cang Li*, Wen-Wei Lin

*Corresponding author for this work

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

In this paper, we present an efficient ΓQR algorithm for solving the linear response eigenvalue problem Hx=λx, where H is Π-symmetric with respect to Γ0=diag(In,−In). Based on newly introduced Γ-orthogonal transformations, the ΓQR algorithm preserves the Π-symmetric structure of H throughout the whole process, and thus guarantees the computed eigenvalues to appear pairwise (λ,−λ) as they should. With the help of a newly established implicit Γ-orthogonality theorem, we incorporate the implicit multi-shift technique to accelerate the convergence of the ΓQR algorithm. Numerical experiments are given to show the effectiveness of the algorithm.

Original languageEnglish
Pages (from-to)191-214
Number of pages24
JournalLinear Algebra and Its Applications
Volume520
DOIs
StatePublished - 1 May 2017

Keywords

  • Linear response eigenvalue problem
  • Structure preserving
  • Γ-orthogonality
  • ΓQR algorithm
  • Π-matrix

Fingerprint Dive into the research topics of 'A symmetric structure-preserving ΓQR algorithm for linear response eigenvalue problems'. Together they form a unique fingerprint.

Cite this