小叠加维度与主动集构造用于在适度误差需求下的多变量积分
Small Superposition Dimension and Active Set Construction for Multivariate Integration Under Modest Error Demand
AI总结：
本文提出一种构造最优或近优主动集的算法，通过实验显示新方法能生成比现有方法更小的主动集，并表明在误差需求不小于10^-3且权重衰减足够快时，叠加维度可能非常小，最多为3。
摘要：
构造主动集是多变量分解方法的关键部分。本文提出了一种构造最优或近优主动集的算法。通过数值实验，显示新方法能提供比现有方法构造的主动集显著更小的集合。实验还表明，当误差需求不小于10^{-3}且权重衰减足够快时，叠加维度可能非常小，最多为3。
英文摘要：
Constructing active sets is a key part of the Multivariate Decomposition Method. An algorithm for constructing optimal or quasi-optimal active sets is proposed in the paper. By numerical experiments, it is shown that the new method can provide sets that are significantly smaller than the sets constructed by the already existing method. The experiments also show that the superposition dimension could surprisingly be very small, at most 3, when the error demand is not smaller than $10^{-3}$ and the weights decay sufficiently fast.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
