Hostname: page-component-f554764f5-qhdkw Total loading time: 0 Render date: 2025-04-11T08:27:42.467Z Has data issue: false hasContentIssue false
  • English
  • Français

Convergence of approximate operator methods for eigenvectors

Published online by Cambridge University Press:  17 April 2009

A. L. Andrew
A. L. Andrew
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 large class of common numerical methods for computing the eigenvectors of a compact linear operator. Special cases include all projection methods and the Weinstein intermediate problems method. Simple sufficient conditions are established for the sequence of approximate eigenvectors obtained by any of these methods to converge to an exact eigenvector. In the most general case only the convergence of a subsequence was proviously known.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 2 , October 1970 , pp. 199 - 205
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Petryshyn, W.V., “On the eigenvalue problem Tu - λSu = 0 with unbounded and nonsymmetric operators T and S”, Philos. Trans. Roy. Soc. London Ser. A 262 (1967/1968), 413–458.Google Scholar
[2]Polskiiˇ, N.I., “On the convergence of certain approximate methods of analysis”, (Russian), Ukrain. Math. Ž. 7 (1955), 56–70.Google Scholar
[3]Fichera, Gaetano, “Approximation and estimates for eigenvalues”. Proc. Sympos. Univ. Maryland, (1965), 317–352. Numerical solution of partial differential equations, edited by Bramble, James H. (Academic Press, New York, London, 1966).Google Scholar
[4]Weinberger, H.F., “Error bounds in the Rayleigh-Ritz approximation of eigenvectors”, J. Res. Nat. Bur. Standards Sect. B 64B (1960), 217–225.CrossRefGoogle Scholar