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Статья
2021

New Sufficient Conditions for the Computation of Generalized Eigenvalues


A. KhellafA. Khellaf, W. MerchelaW. Merchela, H. GuebbaiH. Guebbai
Русская математика
https://doi.org/10.3103/S1066369X21020067
Abstract / Full Text

The purpose of this paper is to give new sufficient conditions for solving numerically a generalized spectrum problem known in the literature as the problem of spectrum approximation of quadratic operator pencils. The new sufficient conditions obtained here are weaker than the norm convergence and the collectively compact convergence, thus they extend some previous results existing in the literature.

Author information
  • Ecole Nationale Polytechnique de Constantine, A New University Town of Ali Mendjeli, BP 75, 25000, Constantine, AlgeriaA. Khellaf
  • Laboratoire des Mathématiques Appliquées et Modélisation, 8 May 1945, BP 401, 24000, Guelma, AlgeriaA. Khellaf, W. Merchela & H. Guebbai
  • Derzhavin Tambov State University, 33 Internatsionalnaya str., 392000, Tambov, RussiaW. Merchela
References
  1. Engstrom, C., Richter, M. “On the spectrum of an operator pencil with applications to wave propagation in periodic and frequency dependent materials”, SIAM J. Appl. Math. 70 (1), 231–247 (2009).
  2. Khellaf, A., Guebbai, H., Lemita, S., Aissaoui, M.Z. “On the Pseudo-spectrum of Operator Pencils”, AsianEuropean J. Math. (2019). doi:10.1142/S1793557120501004.
  3. Khellaf A., Guebbai. H, Lemita S., Aissaoui M.Z. “Eigenvalues computation by the generalized spectrum method of Schrödinger's operator”, Comput. and Appl. Math. 37 (5), 5965–5980 (2018).
  4. Tisseur, F., Meerbergen, K. “The quadratic eigenvalue problem”, SIAM Rev. 43 (2), 235–286 (2001).
  5. Markus, A.S. Introduction to the spectral theory of polynomial operator pencils (in: Translations of Mathematical Monographs, Vol. 71 (American Math. Soc., Prov., RI, 1988)).
  6. Moller, M., Pivovarchik, V. Spectral Theory of Operator Pencils, Hermite–Biehler Functions and their Applications (Birkhäuser, 2015).
  7. Ahues, M., Largillier, A., Limaye, B.V. Spectral computations for bounded operators (Chapman and Hall/CRC, New York, 2001).
  8. Guebbai, H. “Generalized spectrum approximation and numerical computation of Eigenvalues for Schrödinger's Operators”, Lobachevskii J. Math. 34, 45–60 (2013).
  9. Khellaf, A. “New sufficient conditions in the generalized spectrum approach to deal with spectral pollution”, Vestnik Tambovskogo universiteta. Seriya: estestvennye i tekhnicheskie nauki – Tambov University Reports. Series: Natural and Technical Sciences 23 (124), 595–604 (2018).