Application of Linear Prediction for Extrapolating Recursion Coefficients

  • G. Allan
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 58)


The linear prediction theory is used to extrapolate the recursion coefficients and to calculate band limits. The coefficients of the continued fraction are written as sums of complex exponential s. The exponential decays and amplitudes are obtained by a least square fit of the first known coefficients. Application is made to bulk Silicon s and p electronic densities of states. The agreement with an exact one obtained by integration over the Brillouin zone is very good.


Brillouin Zone Linear Prediction Lagrange Multiplier Method Recursion Method Order Perturbation Theory 
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  1. 1.
    See the paper of V. Heine in this volumeGoogle Scholar
  2. 2.
    See the papers in this volume dealing with the asymptotic behaviour of the recursion coefficients and the continued fraction terminationGoogle Scholar
  3. 3.
    J. Makhoul, Proc IEEE 63, 561 (1975)Google Scholar
  4. 4.
    R. Haydock, V. Heine, M.J. Kelly, J.Phys. C 5, 2845 (1972)Google Scholar
  5. 5.
    J.P. Gaspard, F. Cyrot-Lackmann, J.Phys.C 6, 3077 (1973)Google Scholar
  6. 6.
    D.M. Bylander, J.J. Rehr, J.Phys. C 13, 4157 (1980)Google Scholar
  7. 7.
    P. Turchi, F. Ducastelle, G. Treglia, J.Phys.C 15, 2891 (1981)ADSCrossRefGoogle Scholar
  8. 8.
    C.L. Hodges, J.Physique 38, 187 (1977)Google Scholar
  9. 9.
    A. Trias, M. Kiwi, M. Weissmann, Phys.Rev. B28, 1859 (1983)Google Scholar
  10. 10.
    J. Rath, A.J. Freeman, Phys.Rev. B11, 2109 (1975)Google Scholar
  11. 11.
    M.S. Methfessel, M.H. Boon, F.M. Mueller, J.Phys. C 16, L949 (1983)ADSCrossRefGoogle Scholar
  12. 12.
    G. Allan, J. Phys. C 17, 3945 (1984)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • G. Allan
    • 1
  1. 1.Laboratoire de physique des solidesInstitut Supérieur d’Electronique du NordLille CédexFrance

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