论文标题
定制QMC和RQMC点集的工具
A Tool for Custom Construction of QMC and RQMC Point Sets
论文作者
论文摘要
我们提出了Latnet Builder，这是一种软件工具，可在基本2中找到针对晶格规则，多项式晶格规则和数字网的良好参数，用于Quasi-Monte Carlo（QMC）和随机的Quasi-Monte Carlo（RQMC）在$ s $ s $ sugmensional-imensional单位hypercube上进行采样。选择标准是功绩的数字，可为不同的坐标子集提供不同的权重。它们是最坏情况误差（对于QMC）或方差（对于RQMC）的上限，用于集成量的重新定性，以在某些Hilbert功能空间中具有最多的标准。我们总结了Latnet Builder支持的各种Hilbert空间，差异，权重类型，功绩类型，构造类型和搜索方法。我们简要讨论其组织，并提供简单的说明，以说明它可以做什么。
We present LatNet Builder, a software tool to find good parameters for lattice rules, polynomial lattice rules, and digital nets in base 2, for quasi-Monte Carlo (QMC) and randomized quasi-Monte Carlo (RQMC) sampling over the $s$-dimensional unit hypercube. The selection criteria are figures of merit that give different weights to different subsets of coordinates. They are upper bounds on the worst-case error (for QMC) or variance (for RQMC) for integrands rescaled to have a norm of at most one in certain Hilbert spaces of functions. We summarize what are the various Hilbert spaces, discrepancies, types of weights, figures of merit, types of constructions, and search methods supported by LatNet Builder. We briefly discuss its organization and we provide simple illustrations of what it can do.
