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Analysis of a SOR-Like Multi-Grid Algorithm for Eigenvalue Problems

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Advances in Multi-Grid Methods

Part of the book series: Notes on Numerical Fluid Mechanics ((NNFM,volume 11))

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Summary

In the recent years some multi-grid algorithms for the solution of eigenvalue problems have been developed. In this contribution, a SOR-like multi-grid method is proposed and the influence of perturbations in some algorithmic components is analysed. Finally, some practical experiences with this method are referred.

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References

  1. Bank, R.: Analysis of a multilevel inverse iteration procedure for eigenvalue problems. SIAM J. Numer. Anal., Vol. 19, 836–393 (1932).

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  2. Brandt, A., McCormick, S., Ruge, J.: Multigrid methods for differential eigenproblems. SIAM, J. Sci. Statist. Comput. 4, 244–260 (1933).

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  3. Hackbusch, W.: On the computation of approximate eigenvalues and eigenfunctions of elliptic operators by means of a multi-grid method. SIAM J. Numer. Anal., Vol. 16, 201–215 (1979).

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  4. Hackbusch, W., Hofmann, G.: Results of the eigenvalueproblem for the plate equation. Zeitung für Angew. Math. Phys., Vol. 31, 730–739 (1930).

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  5. Hofmann, G.: Analyse eines Mehrgitterverfahrens zur Eigenwertberechnung. Doctoral thesis, Inst. f. Informatik und Prakt. Mathematik, Christian-Albrechts-Universität Kiel, (1985).

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Author information

Authors and Affiliations

  1. Institut für Informatik und Praktische Mathematik, Christian-Albrechts-Universität Kiel, Olshausenstr. 40, D-2300, Kiel 1, Germany

    G. Hofmann

Authors
  1. G. Hofmann
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Editor information

Editors and Affiliations

  1. Bochum, Deutschland

    Dietrich Braess

  2. Kiel, Deutschland

    Wolfgang Hackbusch

  3. St. Augustin, Florida, USA

    Ulrich Trottenberg

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© 1985 Springer Fachmedien Wiesbaden

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Hofmann, G. (1985). Analysis of a SOR-Like Multi-Grid Algorithm for Eigenvalue Problems. In: Braess, D., Hackbusch, W., Trottenberg, U. (eds) Advances in Multi-Grid Methods. Notes on Numerical Fluid Mechanics, vol 11. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14245-4_5

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  • DOI: https://doi.org/10.1007/978-3-663-14245-4_5

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-08085-3

  • Online ISBN: 978-3-663-14245-4

  • eBook Packages: Springer Book Archive

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