Coarse scrambling for Sobol' and Niederreiter sequences
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909821491478528 |
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| author | Suzuki, Kosuke |
| author_facet | Suzuki, Kosuke |
| contents | We introduce \emph{coarse scrambling}, a novel randomization for digital sequences that permutes blocks of digits in a mixed-radix representation. This construction is designed to preserve the powerful $(0,\boldsymbol{e},d)$-sequence property of the underlying points. For sufficiently smooth integrands, we prove that this method achieves the canonical $O(n^{-3+ε})$ variance decay rate, matching that of standard Owen's scrambling. Crucially, we show that its maximal gain coefficient grows only logarithmically with dimension, $O(\log d)$, thus providing theoretical robustness against the curse of dimensionality affecting scrambled Sobol' sequences. Numerical experiments validate these findings and illustrate a practical trade-off: while Owen's scrambling is superior for integrands sensitive to low-dimensional projections, coarse scrambling is competitive for functions with low effective truncation dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02111 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coarse scrambling for Sobol' and Niederreiter sequences Suzuki, Kosuke Numerical Analysis 65C05, 65D30 We introduce \emph{coarse scrambling}, a novel randomization for digital sequences that permutes blocks of digits in a mixed-radix representation. This construction is designed to preserve the powerful $(0,\boldsymbol{e},d)$-sequence property of the underlying points. For sufficiently smooth integrands, we prove that this method achieves the canonical $O(n^{-3+ε})$ variance decay rate, matching that of standard Owen's scrambling. Crucially, we show that its maximal gain coefficient grows only logarithmically with dimension, $O(\log d)$, thus providing theoretical robustness against the curse of dimensionality affecting scrambled Sobol' sequences. Numerical experiments validate these findings and illustrate a practical trade-off: while Owen's scrambling is superior for integrands sensitive to low-dimensional projections, coarse scrambling is competitive for functions with low effective truncation dimension. |
| title | Coarse scrambling for Sobol' and Niederreiter sequences |
| topic | Numerical Analysis 65C05, 65D30 |
| url | https://arxiv.org/abs/2510.02111 |