Published

New analysis of the sphere covering problems and optimal polytope approximation of convex bodies

Long Chen

Journal of Approximation Theory, 133(1):134-145, 2005

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Abstract:

  In this paper, we show that both sphere covering problems and
  optimal polytope approximation of convex bodies are related to
  optimal Delaunay triangulations, which are the triangulations
  minimizing the interpolation error between function $\normx$ and its
  linear interpolant based on the underline triangulations. We then
  develop a new analysis based on the estimate of the interpolation
  error to get the Coxeter-Few-Rogers lower bound for the thickness in
  the sphere covering problem and a new estimate of the constant $\del
  _n $ appeared in the optimal polytope approximation of convex
  bodies.