On Padé approximants and the ε–algorithms for vectors in 2 and 3 dimensions

• Claude Brezinski ^[1]
  1. [1] Universit´e des Sciences et Technologies de Lille
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 3, Nº. 2, 2011, págs. 271-280
• Idioma: inglés
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• Resumen

  • After reminding what Pad´e approximants are and how they can be recursively computed by the ε-algorithm, relations between the results produced by the scalar ε- algorithm applied to a sequence of complex numbers and by the vector ε-algorithm applied to the two-dimensional vectors formed by their real and imaginary parts are given. This result is then extended to sequences of quaternions and threedimensional vectors. Negative results and an open question end the paper.