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Compatibility of Continued Fraction Convergents with Padé Approximants

In: Approximation and Computation

Author

Listed:
  • Jacek Gilewicz

    (Centre de Physique Théorique, CNRS)

  • Radosław Jedynak

    (Politechnika Radomska im. K. Pułaskiego)

Abstract

A Padé approximant (PA) to a function f is a rational function P m ∕ Q n matching the power expansion of f at least up to the (m + n)th power. On the contrary, the convergents of the Stieltjes, Jacobi, or Thiele continued fractions (CF) of f define all PA of f. However, the convergents of general CF are not necessarily PA. In this work, we present the rules stating when the convergents of CF are consistent with PA. The similar problem of compatible transformations of a variable and a function applied to PA was studied in [1].

Suggested Citation

  • Jacek Gilewicz & Radosław Jedynak, 2010. "Compatibility of Continued Fraction Convergents with Padé Approximants," Springer Optimization and Its Applications, in: Walter Gautschi & Giuseppe Mastroianni & Themistocles M. Rassias (ed.), Approximation and Computation, pages 135-144, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-6594-3_10
    DOI: 10.1007/978-1-4419-6594-3_10
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