On the cubic L 1 spline interpolant to the Heaviside function

@article{Auquiert2007OnTC,
  title={On the cubic L 1 spline interpolant to the Heaviside function},
  author={Philippe Auquiert and Olivier Gibaru and Eric Nyiri},
  journal={Numerical Algorithms},
  year={2007},
  volume={46},
  pages={321-332}
}
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. 

Citations

Publications citing this paper.
Showing 1-10 of 11 extracted citations

References

Publications referenced by this paper.
Showing 1-5 of 5 references

Analyse Fonctionnelle: Théorie et Applications

H. Brezis
Dunod, Paris • 1999
View 1 Excerpt

Gibbs phenomenon for best Lp approximation by polygonal lines

Saff, E.B, F. Tashev
East J. Approx. 5(2), 235–251 • 1999
View 1 Excerpt

Convergence and Gibb’s phenomenon in cubic spline interpolation of discontinuous functions

Z. Zhang, C. F. Martin
J. Comput. Appl. Math. 87, 359–371 • 1997
View 1 Excerpt

Similar Papers

Loading similar papers…