Counting Nodes in Smolyak Grids
Combinatorics
2025-04-02 v2 Numerical Analysis
Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2408.09809,
title = {Counting Nodes in Smolyak Grids},
author = {Jocelyn Minini and Micha Wasem},
journal= {arXiv preprint arXiv:2408.09809},
year = {2025}
}
Comments
Final version, 10 pages, 1 figure