论文信息 - On a new method for constructing good point sets on spheres

On a new method for constructing good point sets on spheres

We use quadrature formulas with equal weights in order to constructN point sets on spheres ind-space (d ≥ 3) which are almost optimal with respect to a discrepancy concept, based on distance functions (potentials) and distance functionals (energies). By combining this approach with the probabilistic method, we obtain almost best possible approximations of balls by zonotopes, generated byN segments of equal length.

Gerold Wagner

[1] Gerold Wagner,et al. On means of distances on the surface of a sphere. II. (Upper bounds) , 1990 .

[2] J. Lindenstrauss,et al. Distribution of points on spheres and approximation by zonotopes , 1988 .

[3] J. Beck. Some upper bounds in the theory of irregularities of distribution , 1984 .

[4] E. Bolker. A class of convex bodies , 1969 .

[5] J. Linhart,et al. Approximation of a ball by zonotopes using uniform distribution on the sphere , 1989 .

[6] Peter Sjögren,et al. Estimates of mass distributions from their potentials and energies , 1972 .

[7] Gerold Wagner,et al. On the product of distances to a point set on a sphere , 1989, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[8] K. Stolarsky. Sums of distances between points on a sphere. II , 1972 .

[9] A. Lubotzky,et al. Hecke operators and distributing points on the sphere I , 1986 .

[10] J. Lindenstrauss,et al. Approximation of zonoids by zonotopes , 1989 .

[11] P. McMullen,et al. Estimating the Sizes of Convex Bodies from Projections , 1983 .

[12] Gerold Wagner,et al. On averaging sets , 1991 .