Improving the numerical stability of the Sakurai-Sugiura method for quadratic eigenvalue problems

Research output: Contribution to journalArticle

  • Authors:
  • Hongjia Chen
  • Yasuyuki Maeda
  • Akira Imakura
  • Tetsuya Sakurai
  • Francoise Tisseur

Abstract

The Sakurai-Sugiura method with Rayleigh-Ritz projection (SS-RR method) nds the eigen-values in a certain domain of the complex plane of large quadratic eigenvalue problems (QEPs). The standard implementation of the SS-RR method can suer from numerical instability when the coecient matrices of the projected QEP vary widely in norm. To improve the numerical stability of the SS-RR method, we combine it with a numerically stable eigensolver for the complete solution of the small projected QEP. We analyze the backward stability of the proposed method and show, through numerical experiments, that it computes eigenpairs with backward errors that are smaller than those computed by the standard SS-RR method.

Bibliographical metadata

Original languageEnglish
Pages (from-to)17-20
Number of pages4
JournalJSIAM Letters
Volume9
DOIs
StatePublished - 2017