Compatibility of Continued Fraction Convergents with Padé Approximants

Jacek Gilewicz () and Radosław Jedynak ()
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Jacek Gilewicz: Centre de Physique Théorique, CNRS
Radosław Jedynak: Politechnika Radomska im. K. Pułaskiego

A chapter in Approximation and Computation, 2010, pp 135-144 from Springer

Abstract: 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].

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-6594-3_10

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DOI: 10.1007/978-1-4419-6594-3_10

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