Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
On the number of nodes in n-dimensional cubature formulae of degree 5 for integrals over the ball
Journal of Computational and Applied Mathematics
Cubature formulas in numerical analysis and Euclidean tight designs
European Journal of Combinatorics
New computationally efficient quadrature formulas for pyramidal elements
Finite Elements in Analysis and Design
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A lower bound for positive cubature formulae on the unit ball is given. For the Chebyshev weight function on the ball in R2, the new bound shows that a positive cubature formula of degree s with all nodes inside the ball will need at least Ns≥0.13622s2(1 + O(s-1)) number of nodes, in comparison with the classical lower bound of Ns≥0.125s2(1 + O(s-1)).