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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.04708 |
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| _version_ | 1866908753282990080 |
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| author | An, Congpei Sommariva, Alvise Vianello, Marco |
| author_facet | An, Congpei Sommariva, Alvise Vianello, Marco |
| contents | We compute numerically the $L^2$ Marcinkiewicz-Zygmund constants of cubature rules, with a special attention to their role in polynomial approximation by orthogonal bases. We test some relevant rules on domains such as the interval, the square, the disk, the triangle, the cube and the sphere. The approximation power of the corresponding least squares (LS) projection is compared with standard hyperinterpolation and its recently proposed ``exactness-relaxed'' version. The Matlab codes used for these tests are available in open-source form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04708 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the role of weak Marcinkiewicz-Zygmund constants in polynomial approximation by orthogonal bases An, Congpei Sommariva, Alvise Vianello, Marco Numerical Analysis We compute numerically the $L^2$ Marcinkiewicz-Zygmund constants of cubature rules, with a special attention to their role in polynomial approximation by orthogonal bases. We test some relevant rules on domains such as the interval, the square, the disk, the triangle, the cube and the sphere. The approximation power of the corresponding least squares (LS) projection is compared with standard hyperinterpolation and its recently proposed ``exactness-relaxed'' version. The Matlab codes used for these tests are available in open-source form. |
| title | On the role of weak Marcinkiewicz-Zygmund constants in polynomial approximation by orthogonal bases |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.04708 |