A Tool for Custom Construction of QMC and RQMC Point Sets - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Springer Proceedings in Mathematics & Statistics Année : 2022

A Tool for Custom Construction of QMC and RQMC Point Sets

Résumé

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 sdimensional 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.

Domaines

Calcul [stat.CO]
Fichier principal
Vignette du fichier
mcqmc20latnet.pdf (386.23 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Licence : CC BY SA - Paternité - Partage selon les Conditions Initiales

Dates et versions

hal-03944178 , version 1 (17-01-2023)

Licence

Paternité - Partage selon les Conditions Initiales

Identifiants

Citer

Pierre L’Ecuyer, Pierre Marion, Maxime Godin, Florian Puchhammer. A Tool for Custom Construction of QMC and RQMC Point Sets. Springer Proceedings in Mathematics & Statistics, 2022, Monte Carlo and Quasi-Monte Carlo Methods MCQMC 2020, Oxford, United Kingdom, August 10–14, 387, pp.51-70. ⟨10.1007/978-3-030-98319-2_3⟩. ⟨hal-03944178⟩
8 Consultations
46 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More