Reduced digital nets
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909464424087552 |
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| author | Anupindi, Vishnupriya Kritzer, Peter |
| author_facet | Anupindi, Vishnupriya Kritzer, Peter |
| contents | In the recent papers ``The fast reduced QMC matrix-vector product'' (J. Comput. Appl. Math. 440, 115642, 2024) and ``Column reduced digital nets'' (submitted), it was proposed to use QMC rules based on reduced digital nets which provide a speed-up in the computation of QMC vector-matrix products that may occur in practical applications. In this paper, we provide upper bounds on the quality parameter of row reduced and column-row reduced digital nets, which are helpful for the error analysis of using reduced point sets as integration nodes in a QMC rule. We also give remarks on further aspects and comparisons of row reduced, column reduced, and column-row reduced digital net. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_13659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reduced digital nets Anupindi, Vishnupriya Kritzer, Peter Numerical Analysis In the recent papers ``The fast reduced QMC matrix-vector product'' (J. Comput. Appl. Math. 440, 115642, 2024) and ``Column reduced digital nets'' (submitted), it was proposed to use QMC rules based on reduced digital nets which provide a speed-up in the computation of QMC vector-matrix products that may occur in practical applications. In this paper, we provide upper bounds on the quality parameter of row reduced and column-row reduced digital nets, which are helpful for the error analysis of using reduced point sets as integration nodes in a QMC rule. We also give remarks on further aspects and comparisons of row reduced, column reduced, and column-row reduced digital net. |
| title | Reduced digital nets |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.13659 |