Hostname: page-component-84b7d79bbc-g78kv Total loading time: 0 Render date: 2024-07-29T14:52:57.462Z Has data issue: false hasContentIssue false
  • English
  • Français

Computation of eigenvectors corresponding to multiple eigenvalues

Published online by Cambridge University Press:  17 April 2009

A.L. Andrew  and
G.C. Elton
A.L. Andrew
Affiliation:
La Trobe University, Bundoora, Victoria.
G.C. Elton
Affiliation:
La Trobe University, Bundoora, Victoria.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper examines a class of common numerical methods for computing eigenvectors of a compact linear operator. A necessary and sufficient condition is established for every element of an arbitrary given eigenspace to be the limit of a sequence of the approximate eigenvectors obtained by any given method in this class.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 3 , June 1971 , pp. 419 - 422
Copyright
Copyright © Australian Mathematical Society 1971

References

]Andrew, A.L., “Convergence of approximate operator methods for eigenvectors”, Bull. Austral. Math. Soc. 3 (1970), 199–205.CrossRefGoogle Scholar
[2]Pol'skiĭ, N.I., “On the convergence of certain approximate methods of analysis” (Russian), Ukrain. Math. ž. 7 (1955), 56–70.Google Scholar
[3]Vaĭnikko, G.M., “Asymptotic evaluations of the error of projection methods for the eigenvalue problem” (Russian), ž. Vyčisl. Mat. i Mat. Fiz. 4 (1964), 405–425. English transl. USSR Comput. Math, and Math. Phys. 4 (1964), no. 3, (1966), 9–36.Google Scholar