A distributional finite difference operator obtained from singular integral quadratures achieves spectral accuracy whose rate improves with regularity, without polynomial interpolation or other bases.
WHITTAKER, On the functions which are represented by the ex- pansions of the interpolation theory,Proc
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Singular integration towards a spectrally accurate finite difference operator
A distributional finite difference operator obtained from singular integral quadratures achieves spectral accuracy whose rate improves with regularity, without polynomial interpolation or other bases.