## Abstract

In 2005, Kuperberg proved that 2^{s} points ±^{z1}±^{z2}±⋯±^{zs}^{′} form a Chebyshev-type (2s+1)-quadrature formula on [-1,1] with constant weight if and only if the ^{zi}'s are the zeros of polynomialQ(x)=^{xs}-x^{s-1}3+x^{s-2}45-⋯+(-1) ^{s}1·3·15⋯(4^{s-1}).The Kuperberg's construction on Chebyshev-type quadrature formula above may be regarded as giving an explicit construction of spherical (2s+1)-designs in the Euclidean space of dimension 3. Motivated by the Kuperberg's result, in this paper, we observe an experimental construction of spherical (2s+1)-designs, for certain s, from the Kuperberg set of the form ± a_{1}± a_{2}±⋯± a_{s} in the Euclidean spaces of certain dimensions d≥4.

Original language | English |
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Pages (from-to) | 45-52 |

Number of pages | 8 |

Journal | Applied Mathematics and Computation |

Volume | 249 |

DOIs | |

Publication status | Published - 2014 Dec 15 |

## Keywords

- Chebyshev-type quadrature formula
- Interval designs
- Kuperberg's set
- Spherical designs

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics