Fibonacci 和 Frolov 点集的色散性
Dispersion of the Fibonacci and the Frolov point sets
AI总结：
研究证明Fibonacci和Frolov点集在集合数量增加时色散性衰减最优，为多变量三角多项式子空间的统一范数提供通用离散化方案。
摘要：
证明Fibonacci和Frolov点集在集合数量增加时色散性衰减最优，这表明它们为自然子空间集合的统一范数提供通用离散化。通过新特征——平滑固定体积偏差的上界，推导出色散性的最优上界。证明Fibonacci点集为所有积分范数提供通用离散化。
英文摘要：
It is proved that the Fibonacci and the Frolov point sets, which are known to be very good for numerical integration, have optimal rate of decay of dispersion with respect to the cardinality of sets. This implies that the Fibonacci and the Frolov point sets provide universal discretization of the uniform norm for natural collections of subspaces of the multivariate trigonometric polynomials. It is shown how the optimal upper bounds for dispersion can be derived from the upper bounds for a new characteristic -- the smooth fixed volume discrepancy. It is proved that the Fibonacci point sets provide the universal discretization of all integral norms.
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