A Stable and Accurate Butterfly Sparse Fourier Transform

@article{Kunis2012ASA,
  title={A Stable and Accurate Butterfly Sparse Fourier Transform},
  author={Stefan Kunis and Ines Melzer},
  journal={SIAM J. Numer. Anal.},
  year={2012},
  volume={50},
  pages={1777-1800}
}
Recently, the butterfly approximation scheme was proposed for computing Fourier transforms with sparse and smooth sampling in the frequency and spatial domains. We present a rigorous error analysis which shows how the local expansion degree depends on the target accuracy and the nonharmonic bandwidth. Moreover, we show that the original scheme becomes numerically unstable if a large local expansion degree is used. This problem is removed by representing all approximations in a Lagrange-type… 
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