Advertisement

Multi-Grid Eigenvalue Computation

  • W. Hackbusch
Part of the Notes on Numerical Fluid Mechanics book series (NNFM, volume 11)

Summary

A multi-grid iteration is described, which approximates simultaneously k eigenvalues and the associated vectors. The matrix may be unsymmetric or even not diagonalisable. The algorithm is based on a Newton iteration converging to a kxk sub-matrix of the Schur normal form.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bank, R.A.: Analysis of a multilevel inverse iteration procedure for eigenvalue problems. SIAM J. Numer. Anal. 19 (1982) 886–898.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    Brandt, A., McCormick, S., and J. Ruge: Multigrid methods for differential eigenproblems. SIAM J. Sci. Statist. Comput. 4 (1983) 244–260.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    Chatelin, F.: Simultaneous Newton’s iteration for the Eigenproblem. Computing, Suppl. 5 (1984) 67–74.MathSciNetGoogle Scholar
  4. [4]
    Chatelin, F.: Spectral approximation of linear operators. Academic Press, New York 1983.zbMATHGoogle Scholar
  5. [5]
    Hackbusch, W.: On the computation of approximate eigenvalues and eigenfunctions of elliptic operators by means of a multi-grid method. SIAM J. Numer. Anal. 16 (1979) 201–215.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    Hackbusch, W.: Multi-grid solutions to linear and nonlinear eigenvalue problems for integral and differential equations. Rostock Math. Colloq. 25 (1984) 79–98.MathSciNetzbMATHGoogle Scholar
  7. [7]
    Hackbusch, W.: Multi-Grid Methods. Springer-Verlag, Berlin 1985 (to appear)CrossRefGoogle Scholar
  8. [8]
    Hackbusch, W. and G. Hofmann: Results of the eigenvalue problem for the plate equation. Z. Angew. Math. Phys. 31 (1980) 730–739.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    Hofmann, G.: Analysis eines Mehrgitterverfahrens zur Berechnung von Eigenwerten elliptischer Differentialoperatoren. Doctoral thesis, Kiel 1985.Google Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1985

Authors and Affiliations

  • W. Hackbusch
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-UniversitätKiel 1Germany

Personalised recommendations