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Lobachevskii Journal of Mathematics

, Volume 39, Issue 9, pp 1388–1395 | Cite as

A Note On Generalized Spectrum Approximation

  • Ammar Khellaf
  • Hamza Guebbai
Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
  • 5 Downloads

Abstract

The purpose of this paper is to solve the spectral pollution. We suggest a modern method based on generalized spectral techniques, where we show that the propriety L is hold with norm convergence. In addition, we prove that under collectively compact convergence the proprieties U and L are hold. We describe the theoretical foundations of the method in details, as well as illustrate its effectiveness by numerical results.

Keywords and phrases

spectral pollution generalized spectrum proprieties U and L 

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References

  1. 1.
    E. B. Davies and M. Plum, “Spectral pollution,” arXiv:math/0302145v1 (2002).Google Scholar
  2. 2.
    D. Boffi et al., “On the problem of spurious eigenvalues in the approximation of linear elliptic problems inmixed form,” Math. Comp. 69, 121–140 (1999).CrossRefGoogle Scholar
  3. 3.
    D. Boffi et al., “A remark on spurious eigenvalues in a square,” Appl. Math. Lett. 12, 107–114 (1999).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    A. J. Laub, Matrix Analysis for Scientists and Engineers (SIAM, California, 2005).CrossRefzbMATHGoogle Scholar
  5. 5.
    I. Gohberg, S. Goldberg, and M. A. Kaashoek, Classes of Linear Operators (Springer, Basel AG, 1990), Vol. 1.CrossRefzbMATHGoogle Scholar
  6. 6.
    H. Guebbai, “Generalized Spectrum Approximation and Numerical Computation of Eigenvalues for Schrödinger’s Operators 45, 60,” Lobachevskii J. Math. 34 (1) (2013).Google Scholar
  7. 7.
    M. Ahues, A. Largillier, and B. V. Limaye, Spectral Computations for Bounded Operators (Chapman and Hall/CRC, New York, 2001).CrossRefzbMATHGoogle Scholar
  8. 8.
    K. E. Atkinson, TheNumerical Solution of Integral Equations of the Second Kind (Cambridge Univ. Press, Cambridge, 1997).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Laboratoire des Mathmatiques Appliques et ModlisationUniversité de 8 Mai 1945 de GuelmaGuelmaAlgeria

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