Counting Nodes in Smolyak Grids
<|reference_start|>Counting Nodes in Smolyak Grids: 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, M\"uller-Gronbach, Novak-Ritter and Ullrich.<|reference_end|>
@article{minini2024counting,
    title={Counting Nodes in Smolyak Grids},
    author={Jocelyn Minini and Micha Wasem},
    journal={arXiv preprint arXiv:2408.09809},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.09809},
    primaryClass={math.CO cs.NA math.NA}
}