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).