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The Effect of a Postprocessing Procedure to Upper Bounds of the Eigenvalues

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Numerical Methods and Applications (NMA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8962))

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Abstract

This paper presents a postprocessing technique applied to second- and fourth-order eigenvalue problems. It has been proved that this approach always ensures asymptotically upper bounds for corresponding eigenvalues. The main goal could be formulated as follows: if nonconforming finite elements are used giving lower bounds of eigenvalues, then the presented algorithm is a simple approach for obtaining two-sided bounds of eigenvalues; if conforming finite elements are used by origin, the postprocessing algorithm gives improved approximations of the eigenvalues, which remain asymptotically greater than the exact ones.

Some different aspects of the method applicability are also discussed. Finally, computer based implementations are presented.

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References

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Acknowledgement

This work is partially supported by the Bulgarian NSF grant DFNI-I 01/5.

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Authors and Affiliations

  1. Institute of Information and Communication Technologies, BAS, Sofia, Bulgaria

    A. B. Andreev

  2. Technical University of Gabrovo, Gabrovo, Bulgaria

    M. R. Racheva

Authors
  1. A. B. Andreev
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  2. M. R. Racheva
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Corresponding author

Correspondence to M. R. Racheva .

Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stefka Fidanova

  3. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

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© 2015 Springer International Publishing Switzerland

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Andreev, A.B., Racheva, M.R. (2015). The Effect of a Postprocessing Procedure to Upper Bounds of the Eigenvalues. In: Dimov, I., Fidanova, S., Lirkov, I. (eds) Numerical Methods and Applications. NMA 2014. Lecture Notes in Computer Science(), vol 8962. Springer, Cham. https://doi.org/10.1007/978-3-319-15585-2_31

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  • DOI: https://doi.org/10.1007/978-3-319-15585-2_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15584-5

  • Online ISBN: 978-3-319-15585-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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