A Tool for Custom Construction of QMC and RQMC Point Sets
A Tool for Custom Construction of QMC and RQMC Point Sets
复制标题
用于定制构建 QMC 和 RQMC 点集的工具
DOI：
10.1007/978-3-030-98319-2_3
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
F. Puchhammer
中科院分区：
文献类型：
--
作者：
P. L'Ecuyer;P. Marion;Maxime Godin;F. Puchhammer
我们提出了LatNet Builder，一个软件工具，以找到良好的参数格规则，多项式格规则，数字网在基地2，准蒙特卡罗（QMC）和随机准蒙特卡罗（RQMC）抽样在这些维单位超立方体。选择标准是对不同的坐标子集给予不同权重的品质因数。它们是最坏情况下的误差（对于QMC）或方差（对于RQMC）的上界，被积函数在某些希尔伯特函数空间中被重新标度为至多为1的范数。我们总结了LatNet Builder支持的各种希尔伯特空间、差异、权重类型、品质因数、构造类型和搜索方法。我们简要地讨论了它的组织，并提供了它可以做什么的简单说明。
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 thes-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.