Optimal logarithmic energy points on the unit sphere

@article{Brauchart2008OptimalLE,
  title={Optimal logarithmic energy points on the unit sphere},
  author={Johann S. Brauchart},
  journal={Math. Comput.},
  year={2008},
  volume={77},
  pages={1599-1613}
}
We study minimum energy point charges on the unit sphere Sd in Rd+1, d ≥ 3, that interact according to the logarithmic potential log(1/r), where r is the Euclidean distance between points. Such optimal N-point configurations are uniformly distributed as N → ∞. We quantify this result by estimating the spherical cap discrepancy of optimal energy configurations. The estimate is of order O(N−1/(d+2)). Essential is an improvement of the lower bound of the optimal logarithmic energy which yields the… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 24 references

Estimates of mass distributions from their potentials and energies

  • P. Sjögren
  • Ark. Mat. 10
  • 1026
Highly Influential
3 Excerpts

Fekete extreme points and related problems

  • J. Korevaar
  • Approximation theory and function series…
  • 1004
Highly Influential
3 Excerpts

Stegun (eds.), Handbook of mathematical functions with formulas, graphs, and mathematical tables

  • I.A.M. Abramowitz
  • 1970

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