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Mathematical Notes

, Volume 79, Issue 1–2, pp 41–54 | Cite as

Berlekamp—Massey Algorithm, Continued Fractions, Pade Approximations, and Orthogonal Polynomials

  • S. B. Gashkov
  • I. B. Gashkov
Article

Abstract

The Berlekamp—Massey algorithm (further, the BMA) is interpreted as an algorithm for constructing Pade approximations to the Laurent series over an arbitrary field with singularity at infinity. It is shown that the BMA is an iterative procedure for constructing the sequence of polynomials orthogonal to the corresponding space of polynomials with respect to the inner product determined by the given series. The BMA is used to expand the exponential in continued fractions and calculate its Pade approximations.

Key words

Berlekamp—Massey algorithm Pade approximations continued fraction orthogonal polynomial Laurent series Euclid's algorithm 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • S. B. Gashkov
    • 1
  • I. B. Gashkov
    • 2
  1. 1.M. V. Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Karlstads UniversitetSweden

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