Continuous methods for extreme and interior eigenvalue problems

Gene H. Golub, Lizhi LIAO*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

In this paper, continuous methods are introduced to compute both the extreme and interior eigenvalues and their corresponding eigenvectors for real symmetric matrices. The main idea is to convert the extreme and interior eigenvalue problems into some optimization problems. Then a continuous method which includes both a merit function and an ordinary differential equation (ODE) is introduced for each resulting optimization problem. The convergence of each ODE solution is proved for any starting point. The limit of each ODE solution for any starting point is fully studied. Both the extreme and the interior eigenvalues and their corresponding eigenvectors can be easily obtained under a very mild condition. Promising numerical results are also presented.

Original languageEnglish
Pages (from-to)31-51
Number of pages21
JournalLinear Algebra and Its Applications
Volume415
Issue number1
DOIs
Publication statusPublished - 1 May 2006

Scopus Subject Areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

User-Defined Keywords

  • Continuous method
  • Eigenvalue
  • Eigenvector

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