Interpolation, approximation and rational extrapolation : Rational approximation

Rational approximation
Interpolation, approximation and rational extrapolation

Authors : Claude BREZINSKI, Michela REDIVO-ZAGLIA

Publication date: October 10, 2013 | Lire en français

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2. Rational approximation

Let f be a function for which the first terms of the Taylor series at 0 are known, whether or not the series is convergent.

f (x) = c_{0} + c_{1} x + c_{2} x^{2} + \dots

We'll show how it's possible to construct rational fractions whose development in series coincides with that of f up to a certain order.

We want to construct a rational fraction, with a numerator of degree p and a denominator...

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Ongoing reading
Rational approximation

(1) - BAKER (G.A.) Jr., GRAVES-MORRIS (P.R.) - Padé Approximants - 2^nd ed., Cambridge University Press, Cambridge (1996).
(2) - BERRUT (J.-P.), BALTENSPERGER (R.), MITTELMANN (H.D.) - . – Recent developments in barycentric rational interpolation,...

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