Error and stability estimates for surface-divergence free RBF interpolants on the sphere

@article{Fuselier2009ErrorAS,
  title={Error and stability estimates for surface-divergence free RBF interpolants on the sphere},
  author={Edward J. Fuselier and Francis J. Narcowich and Joseph D. Ward and Grady B. Wright},
  journal={Math. Comput.},
  year={2009},
  volume={78},
  pages={2157-2186}
}
Recently, a new class of surface-divergence free radial basis function interpolants has been developed for surfaces in R3. In this paper, several approximation results for this class of interpolants will be derived in the case of the sphere, S2. In particular, Sobolev-type error estimates are obtained, as well as optimal stability estimates for the associated interpolation matrices. In addition, a Bernstein estimate and an inverse theorem are also derived. Numerical validation of the… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 58 references

Constructive approximation on the sphere, Numerical Mathematics and Scientific Computation

  • W. Freeden, T. Gervens, M. Schreiner
  • With applications to geomathematics
  • 1998
Highly Influential
3 Excerpts

Gilkey , The index theorem and the heat equation

  • B. Peter
  • Adv . Comp . Math .
  • 2008

Interpolation and cubature on the sphere, accessed 2008, http://web.maths.unsw.edu.au/~rsw/Sphere

  • R. S. Womersley, I. H. Sloan
  • 2008
2 Excerpts

, Xingping Sun , Joseph D . Ward , and Holger Wendland , Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions , Found

  • J. Francis
  • Comput . Math .
  • 2007

Divergence - free RBFs on surfaces

  • Shmuel Rippa
  • J . Fourier Anal . Appl .
  • 2007

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