<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We propose a notion of (<bold>t</bold>, <bold>e</bold>, <italic>s</italic>)-sequences in multiple bases, which unifies the Halton sequence and (<italic>t, s</italic>)-sequences under one roof, and obtain an upper bound of their discrepancy consisting only of the leading term. By using this upper bound, we improve the tractability results currently known for the Halton sequence, the Niederreiter sequence, the Sobol’ sequence, and the generalized Faure sequence, and also give tractability results for the Xing-Niederreiter sequence and the Hofer-Niederreiter sequence, for which no results have been known so far.</p></abstract>

We propose a notion of (t, e, s)-sequences in multiple bases, which unifies the Halton sequence and (t, s)-sequences under one roof, and obtain an upper bound of their discrepancy consisting only of the leading term. By using this upper bound, we improve the tractability results currently known for the Halton sequence, the Niederreiter sequence, the Sobol’ sequence, and the generalized Faure sequence, and also give tractability results for the Xing-Niederreiter sequence and the Hofer-Niederreiter sequence, for which no results have been known so far.

Tractability of Multivariate Integration Using Low-Discrepancy Sequences

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Tractability of Multivariate Integration Using Low-Discrepancy Sequences"}

We propose a notion of (t, e, s)-sequences in multiple bases, which unifies the Halton sequence and (t, s)-sequences under one roof, and obtain an upper bound...

Tractability of Multivariate Integration Using Low-Discrepancy Sequences

Publié en ligne: 13 janv. 2017

Pages: 23 - 43

Reçu: 23 nov. 2015

Accepté: 30 avr. 2016

DOI: https://doi.org/10.1515/udt-2016-0013

Mots clés
discrepancy, low-discrepancy sequences, multivariate integration, tractability, (, , )-sequences

© 2016 Shu Tezuka, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Tractability of Multivariate Integration Using Low-Discrepancy Sequences

Publié en ligne: 13 janv. 2017

Pages: 23 - 43

Reçu: 23 nov. 2015

Accepté: 30 avr. 2016

DOI: https://doi.org/10.1515/udt-2016-0013

Mots clésdiscrepancy, low-discrepancy sequences, multivariate integration, tractability, (, , )-sequences

© 2016 Shu Tezuka, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
discrepancy, low-discrepancy sequences, multivariate integration, tractability, (, , )-sequences