A Tool for Custom Construction of QMC and RQMC Point Sets

Autor:	L'Ecuyer, Pierre, Marion, Pierre, Godin, Maxime, Puchhammer, Florian
Rok vydání:	2020
Předmět:	Statistics - Computation Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	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. Comment: 19 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2012.10263 Zobrazit plný text záznamu View this record from Arxiv