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Numerische Mathematik

, Volume 89, Issue 3, pp 535–560 | Cite as

Recursive computation of Padé–Legendre approximants and some acceleration properties

  • Ana C. Matos
Original article

Summary.

In this paper, after recalling the two definitions of the generalizations of the Padé approximants to orthogonal series, we will define the Padé–Legendre approximants of a Legendre series. We will propose two algorithms for the recursive computation of some sequences of these approximants. We will also estimate the speed of convergence of the columns of the Padé–Legendre table from the asymptotic behaviour of the coefficients of the Legendre series. Finally we will illustrate these results with some numerical examples.

Mathematics Subject Classification (1991): 33C45, 41A20, 41A21, 41A25, 42C05, 42C10 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ana C. Matos
    • 1
  1. 1.Laboratoire d'Analyse Numérique et d'Optimisation, UFR IEEA – M3, Université des Sciences et Technologies de Lill, 59655 – Villeneuve d'Ascq Cedex, France; e-mail: matos@ano.univ-lille1.fr FR

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