Solving singular generalized eigenvalue problems by a rank-completing perturbation

Michiel E. Hochstenbach, Christian Mehl, Bor Plestenjak

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
13 Downloads (Pure)

Abstract

Generalized eigenvalue problems involving a singular pencil are very challenging to solve, with respect to both accuracy and efficiency. The existing package Guptri is very elegant but may be time-demanding, even for small and medium-sized matrices. We propose a simple method to compute the eigenvalues of singular pencils, based on one perturbation of the original problem of a certain specific rank. For many problems, the method is both fast and robust. This approach may be seen as a welcome alternative to staircase methods.

Original languageEnglish
Pages (from-to)1022-1046
Number of pages25
JournalSIAM Journal on Matrix Analysis and Applications
Volume40
Issue number3
DOIs
Publication statusPublished - 5 Sep 2019

Keywords

  • Differential algebraic equations
  • Double eigenvalues
  • Guptri
  • Model updating
  • Quadratic two-parameter eigenvalue problem
  • Rank-completing perturbation
  • Singular generalized eigenvalue problem
  • Singular pencil
  • Two-parameter eigenvalue problem

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