The Sobol' sequence is not quasi-uniform in dimension 2
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916102720716800 |
|---|---|
| author | Goda, Takashi |
| author_facet | Goda, Takashi |
| contents | Are common quasi-Monte Carlo sequences quasi-uniform? While this question remains widely open, in this short note, we prove that the two-dimensional Sobol' sequence is not quasi-uniform. This result partially answers an unsolved problem of Sobol' and Shukhman (2007) in a negative manner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05830 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Sobol' sequence is not quasi-uniform in dimension 2 Goda, Takashi Numerical Analysis Are common quasi-Monte Carlo sequences quasi-uniform? While this question remains widely open, in this short note, we prove that the two-dimensional Sobol' sequence is not quasi-uniform. This result partially answers an unsolved problem of Sobol' and Shukhman (2007) in a negative manner. |
| title | The Sobol' sequence is not quasi-uniform in dimension 2 |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2311.05830 |