1. Counting Nodes in Smolyak Grids
- Author
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Minini, Jocelyn and Wasem, Micha
- Subjects
Mathematics - Combinatorics ,Mathematics - 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., Comment: 10 pages, 1 figure
- Published
- 2024