Abstract

The problem of minimizing the energy of a system of \(N\) points on a sphere in \({{\mathbb{R}}^{3}}\), interacting with the potential \(U = \tfrac{1}{{{{r}^{s}}}}\), \(s > 0\), where \(r\) is the Euclidean distance between a pair of points, is considered. A method of projective coordinate descent using a fast calculation of the function and the gradient, as well as a second-order coordinate descent method that rapidly approaches the minimum values known from the literature is proposed.

中文翻译：

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在Fekete问题中使用投影坐标下降

摘要

最小化\（{{\ mathbb {R}} ^ {3}} \）中球面上的\（N \）个点的系统的能量，并与势\（U = \ tfrac {1 } {{{{r} ^ {s}}}} \），\（s> 0 \），其中\（r \）是一对点之间的欧几里得距离。提出了一种使用函数和梯度的快速计算的投影坐标下降方法以及一种快速逼近文献中已知最小值的二阶坐标下降方法。