Counting Nodes in Smolyak Grids
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915221961965568 |
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| author | Minini, Jocelyn Wasem, Micha |
| author_facet | Minini, Jocelyn Wasem, Micha |
| contents | Using generating functions, we are proposing a unified approach to produce explicit formulas, which count the number of nodes in Smolyak grids based on various univariate quadrature or interpolation rules. Our approach yields, for instance, a new formula for the cardinality of a Smolyak grid, which is based on Chebyshev nodes of the first kind and it allows to recover certain counting-formulas previously found by Bungartz-Griebel, Kaarnioja, Müller-Gronbach, Novak-Ritter and Ullrich. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09809 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting Nodes in Smolyak Grids Minini, Jocelyn Wasem, Micha Combinatorics Numerical Analysis 05A15, 05C69, 65D15 Using generating functions, we are proposing a unified approach to produce explicit formulas, which count the number of nodes in Smolyak grids based on various univariate quadrature or interpolation rules. Our approach yields, for instance, a new formula for the cardinality of a Smolyak grid, which is based on Chebyshev nodes of the first kind and it allows to recover certain counting-formulas previously found by Bungartz-Griebel, Kaarnioja, Müller-Gronbach, Novak-Ritter and Ullrich. |
| title | Counting Nodes in Smolyak Grids |
| topic | Combinatorics Numerical Analysis 05A15, 05C69, 65D15 |
| url | https://arxiv.org/abs/2408.09809 |