Frobenius–Padé approximants of |x|

  1. Bello-Hernández, M. 1
  2. Santos-Touza, C. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 IES Huarte, Carretera de Olaz-Txipi, s/n, Huarte, Navarra, Spain
Journal:
Journal of Approximation Theory

ISSN: 0021-9045

Year of publication: 2016

Volume: 211

Pages: 1-15

Type: Article

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DOI: 10.1016/J.JAT.2016.07.002 SCOPUS: 2-s2.0-84982757546 WoS: WOS:000384954300001 GOOGLE SCHOLAR

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Abstract

We construct the Frobenius–Padé approximants of the function |x| in (−1,1) for the Chebyshev weight. These rational functions are linked with the Frobenius–Padé approximants of the function x in (0,1). We prove geometric convergence of the approximants of |x| in C∖{z:ℜ(z)=0}. © 2016 Elsevier Inc.