Quasi-Monte Carlo with a Hankel random digital net
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914509855129600 |
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| author | Goda, Takashi Liu, Yang Tempone, Raúl |
| author_facet | Goda, Takashi Liu, Yang Tempone, Raúl |
| contents | This paper proposes a new randomized design of digital nets in which the generating matrices are chosen to be random Hankel matrices. Compared with previous randomized designs of digital nets, this approach simplifies the construction process and reduces the number of random variables required, while still achieving desirable convergence rates when combined with appropriate estimators. We analyze the properties of the proposed design, derive bounds for Walsh coefficients, and provide error analysis for both the median-of-means estimator and a newly proposed greedy selection estimator, i.e. the selection of the best design from a batch in terms of a worst-case error bound. Numerical experiments validate our theoretical findings and demonstrate the practical performance of the proposed methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24105 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasi-Monte Carlo with a Hankel random digital net Goda, Takashi Liu, Yang Tempone, Raúl Numerical Analysis 65C05, 65D30, 65D32 This paper proposes a new randomized design of digital nets in which the generating matrices are chosen to be random Hankel matrices. Compared with previous randomized designs of digital nets, this approach simplifies the construction process and reduces the number of random variables required, while still achieving desirable convergence rates when combined with appropriate estimators. We analyze the properties of the proposed design, derive bounds for Walsh coefficients, and provide error analysis for both the median-of-means estimator and a newly proposed greedy selection estimator, i.e. the selection of the best design from a batch in terms of a worst-case error bound. Numerical experiments validate our theoretical findings and demonstrate the practical performance of the proposed methods. |
| title | Quasi-Monte Carlo with a Hankel random digital net |
| topic | Numerical Analysis 65C05, 65D30, 65D32 |
| url | https://arxiv.org/abs/2604.24105 |