New analysis of the sphere covering problems and optimal polytope approximation of convex bodies
نویسنده
چکیده
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 ‖x‖2 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-FewRogers lower bound for the thickness in the sphere covering problem and a new estimate of the constant deln appeared in the optimal polytope approximation of convex bodies.
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ورودعنوان ژورنال:
- Journal of Approximation Theory
دوره 133 شماره
صفحات -
تاریخ انتشار 2005