On the cubic L 1 spline interpolant to the Heaviside function

  title={On the cubic L 1 spline interpolant to the Heaviside function},
  author={Philippe Auquiert and Olivier Gibaru and Eric Nyiri},
  journal={Numerical Algorithms},
We prove that the univariate interpolating cubic L 1 spline to the Heaviside function at three sites to the left of the jump and three sites to the right of the jump entirely agrees with the Heaviside function except in the middle interval where it is the interpolating cubic with zero slopes at the end point. This shows that there is no oscillation near the discontinuous point i.e. no Gibbs’ phenomenon. 


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