New representations of Padé, Padé-type, and partial Padé approximants

• Claude Brezinski ^[2] ; Michela Redivo-Zaglia ^[1]
  1. [1] University of Padua

     University of Padua

     Padova, Italia

     
  2. [2] Université des Sciences et Technologies de Lille, France
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 284, Nº 1 (15 August 2015), 2015, págs. 69-77
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.07.007
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• Resumen

  • Padé approximants are rational functions, with a denominator which does not vanish at zero, and whose series expansion match a given series as far as possible. These approximants are usually written under a rational form. In this paper, we will show how to write them also under two different barycentric forms, and under a partial fraction form, depending on free parameters. According to the choice of these parameters, Padé-type approximants can be obtained under a barycentric or a partial fraction form.