一种低加权星差的多项式格点集快速构造方法
A reduced fast construction of polynomial lattice point sets with low weighted star discrepancy
AI总结：
本文提出了一种通过限制多项式集合大小来降低构造多项式格点集生成向量成本的方法，利用空间权重快速衰减的特性，以提高准蒙特卡洛算法的数值积分性能。
摘要：
加权星差是衡量准蒙特卡洛算法中点集性能的定量指标。我们考虑了可以通过逐个组件构造来确保小加权星差的多项式格点集。我们的目标是通过限制所选向量组件的多项式集合大小，显著降低此类生成向量的构造成本。为了实现这一降低，我们利用所考虑的空间权重衰减非常快的特性。
英文摘要：
The weighted star discrepancy is a quantitative measure for the performance of point sets in quasi-Monte Carlo algorithms for numerical integration. We consider polynomial lattice point sets, whose generating vectors can be obtained by a component-by-component construction to ensure a small weighted star discre-pancy. Our aim is to significantly reduce the construction cost of such generating vectors by restricting the size of the set of polynomials from which we select the components of the vectors. To gain this reduction we exploit the fact that the weights of the spaces we consider decay very fast.
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