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Are there techniques to form a Pade approximation (or Pade-like approximation), except force the poles of the rational function to be negative?

I am trying to use Pade approximations to extrapolate a curve based on known derivatives of the curve at a point. The Pade approximation usually does much better than a Taylor series. However, occasionally the Pade approximation creates a spurious pole in the direction I'm extrapolating in, and in this case the approximation is much worse because of the spurious pole.

Has this been studied? I looked around and couldn't find much practical information on this. What do people normally do to avoid spurious poles in Pade approximations?

I would be happy with losing some accuracy in the approximation, if this ensures that the poles are negative (i.e., behind the "starting point" for the curve).

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  • $\begingroup$ An interesting question! I doubt you’ll have a Padé approximant, but maybe your interest is in rational approximation. $\endgroup$ May 23 at 13:46
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    $\begingroup$ You can google barycentric rational interpolation, and also Floater-Hoermann interpolation, which is a rational interpolation without poles. $\endgroup$
    – davidhigh
    May 24 at 6:39

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