Archive for Rational Mechanics and Analysis

, Volume 81, Issue 3, pp 279–287

A convergent variational method of eigenvalue approximation

  • W. M. Greenlee


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aronszajn, N., Approximation methods for eigenvalues of completely continuous symmetric operators. Proceedings of the Symposium on Spectral Theory and Differential Problems, pp. 179–202. Oklahoma: Stillwater 1951.Google Scholar
  2. 2.
    Bazley, N. W., & D. W. Fox, Truncations in the method of intermediate problems for lower bounds to eigenvalues. J. Res. Nat. Bur. of Standards 65B, 105–111 (1961).Google Scholar
  3. 3.
    Bazley, N. W., & D. W. Fox, Comparison operators for lower bounds to eigenvalues. J. Reine Angew. Math. 223, 142–149 (1966).Google Scholar
  4. 4.
    Brown, R. D., Variational approximation methods for eigenvalues. Convergence theorems. Proceedings of the Banach International Mathematical Center. Warsaw; to appear.Google Scholar
  5. 5.
    Fox, D. W., & J. T. Stadter, An eigenvalue estimation method of Weinberger and Weinstein's intermediate problems. SIAM J. Math. Anal. 8, 491–503 (1977).Google Scholar
  6. 6.
    Gould, S. H., Variational Methods for Eigenvalue Problems. 2nd ed. Toronto: Univ. of Toronto Press 1966.Google Scholar
  7. 7.
    Kato, T., Perturbation Theory for Linear Operators. Berlin-Heidelberg-New York: Springer 1966.Google Scholar
  8. 8.
    Riesz, F., & B. Sz.-Nagy, Functional Analysis. New York: Ungar 1955.Google Scholar
  9. 9.
    Simon, B., Lower semicontinuity of positive quadratic forms. Proc. Roy. Soc. Edinburgh 79A, 267–273 (1977).PubMedGoogle Scholar
  10. 10.
    Simon, B., A canonical decomposition for quadratic forms with applications to monotone convergence theorems. J. Functional Analysis 28, 377–385 (1978).Google Scholar
  11. 11.
    Weidmann, J., Monotone continuity of the spectral resolution and the eigenvalues. Proc. Roy. Soc. Edinburgh 85A, 131–136 (1980).Google Scholar
  12. 12.
    Weinberger, H. F., A theory of lower bounds for eigenvalues. Tech. Note BN-103, Inst. for Fluid Dynamics and Applied Mathematics, Univ. of Maryland. Maryland: College Park 1959.Google Scholar
  13. 13.
    Weinberger, H. F., Variational Methods for Eigenvalue Approximation. Philadelphia: SIAM 1974.Google Scholar
  14. 14.
    Weinstein, A., On the base problem for a compact integral operator. J. Math. Mech. 17, 217–223 (1967).Google Scholar
  15. 15.
    Weinstein, A., & W. Stenger, Methods of Intermediate Problems for Eigenvalues. New York-London: Academic Press 1972.Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • W. M. Greenlee
    • 1
  1. 1.Department of Mathematics and Committee on Applied MathematicsUniversity of ArizonaTucson

Personalised recommendations