Fast and Stable Rational Interpolation in Roots of Unity and Chebyshev Points

@article{Pachn2012FastAS,
  title={Fast and Stable Rational Interpolation in Roots of Unity and Chebyshev Points},
  author={Ricardo Pach{\'o}n and Pedro Gonnet and Joris Van Deun},
  journal={SIAM J. Numer. Anal.},
  year={2012},
  volume={50},
  pages={1713-1734}
}
A new method for interpolation by rational functions of prescribed numerator and denominator degrees is presented. When the interpolation nodes are roots of unity or Chebyshev points, the algorithm is particularly simple and relies on discrete Fourier transform matrices, which results in a fast implementation using the fast Fourier transform. The method is generalized for arbitrary grids, which requires the construction of polynomials orthogonal on the set of interpolation nodes. The appearance… 
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