On the Global Optimality of Fibonacci Lattices in the Torus
Nicolas Nagel
我们使用线性编程边界来分析图中关于差异理论和准蒙特卡洛方法中问题的最优性。 这些概念将统一引入张量产品能量。 我们表明,任何维度的规范三点格位在托鲁的所有3点组中都是全球最优的,相对于一大类这样的能量。 这是一个普遍最优的新实例,这种特殊现象只以一小类高度结构化的点集而闻名。 在d=2维度的情况下,推测所谓的斐波那契晶格也应该是相对于一大类潜力的最佳选择。 为此,我们表明5点斐波那契晶格在全球范围内是最佳的,用于与准蒙特卡罗方法分析相关的连续参数化级潜力。
We use linear programming bounds to analyze point sets in the torus with respect to their optimality for problems in discrepancy theory and quasi-Monte Carlo methods. These concepts will be unified by introducing tensor product energies. We show that the canonical 3-point lattice in any dimension is globally optimal among all 3-point sets in the torus with respect to a large class of such energies. This is a new instance of universal optimality, a special phenomenon that is only known for a smal...
