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Mat. Zametki, 2006, Volume 79, Issue 1, Pages 45–59 (Mi mz2673)  

This article is cited in 2 scientific papers (total in 2 papers)

Berlekamp–Massey Algorithm, Continued Fractions, Padé Approximations, and Orthogonal Polynomials

S. B. Gashkova, I. B. Gashkovb

a M. V. Lomonosov Moscow State University
b Karlstads University

Abstract: The Berlekamp–Massey algorithm (further, the BMA) is interpreted as an algorithm for constructing Padé 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.

DOI: https://doi.org/10.4213/mzm2673

Full text: PDF file (240 kB)
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English version:
Mathematical Notes, 2006, 79:1, 41–54

Bibliographic databases:

UDC: 517.51
Received: 16.02.2005

Citation: S. B. Gashkov, I. B. Gashkov, “Berlekamp–Massey Algorithm, Continued Fractions, Padé Approximations, and Orthogonal Polynomials”, Mat. Zametki, 79:1 (2006), 45–59; Math. Notes, 79:1 (2006), 41–54

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. V. Khristoforov, “On uniform approximation of elliptic functions by Padé approximants”, Sb. Math., 200:6 (2009), 923–941  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Padé approximants, continued fractions, and orthogonal polynomials”, Russian Math. Surveys, 66:6 (2011), 1049–1131  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математические заметки Mathematical Notes
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