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Utilisation de l’invariance Homographique dans les Algorithmes de Losange

Part of the Lecture Notes in Mathematics book series (LNM,volume 1071)

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L’objet de ce papier est de caractériser la classe des algorithmes de losange qui vérifient une certaine propriété d’invariance homographique. Cette propriété permet en effet de définir des variantes qui améliorent notablement la fiabilité et la stabilité numérique de ces algorithmes. Parmi les algorithmes satisfaisant cette propriété on trouve des algorithmes d’interpolation rationnelle, l’ε-et le ρ-algorithmes ainsi que plusieurs de leurs généralisations. En particulier une nouvelle forme du ρ-algorithme est dérivée des algorithmes de Stoer et Larkin.

Key Words

  • Algorithmes de losange
  • interpolation rationnelle
  • algorithme de type ϑ
  • invariance homographique
  • ε-algorithme
  • ε-algorithme généralisé
  • ρ-algorithme
  • algorithme de Stoer et Larkin
  • table de Padé
  • fiabilité
  • stabilité numérique

Key Words

  • Rhombus algorithms
  • rational interpolation
  • ϑ-type algorithm
  • homographic invariance property
  • ε-algorithm
  • generalized ε-algorithm
  • ρ-algorithm
  • Stoer-Larkin algorithm
  • Padé Table
  • reliability
  • numerical stability

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© 1984 Springer-Verlag

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Cordellier, F. (1984). Utilisation de l’invariance Homographique dans les Algorithmes de Losange. In: Werner, H., Bünger, H.J. (eds) Padé Approximation and its Applications Bad Honnef 1983. Lecture Notes in Mathematics, vol 1071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099610

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  • DOI: https://doi.org/10.1007/BFb0099610

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  • Print ISBN: 978-3-540-13364-3

  • Online ISBN: 978-3-540-38914-9

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