# 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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