Controllability of matrix eigenvalue algorithms: The inverse power method

U. Helmke, P. A. Fuhrmann

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

In this paper we initiate a program to study the controllability properties of matrix eigenvalue algorithms arising in numerical linear algebra. Our focus is on a well-known eigenvalue method, the inverse power iteration defined on projective space. A complete characterization of the reachable sets and their closures is given via cyclic invariant subspaces. Moreover, a necessary and sufficient condition for almost controllability of the inverse power method is derived.

Original languageEnglish
Pages (from-to)57-66
Number of pages10
JournalSystems and Control Letters
Volume41
Issue number1
DOIs
StatePublished - 15 Sep 2000

Keywords

  • Controllability
  • Eigenvalue method
  • Invariant subspaces
  • Projective space

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