A survey on spherical designs and algebraic combinatorics on spheres
European Journal of Combinatorics
A variational characterisation of spherical designs
Journal of Approximation Theory
Well Conditioned Spherical Designs for Integration and Interpolation on the Two-Sphere
SIAM Journal on Numerical Analysis
Minimizing the Condition Number of a Gram Matrix
SIAM Journal on Optimization
Numerical integration with polynomial exactness over a spherical cap
Advances in Computational Mathematics
Verified error bounds for real solutions of positive-dimensional polynomial systems
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
| Hi-index | 0.00 |
This paper is concerned with proving the existence of solutions to an underdetermined system of equations and with the application to existence of spherical $t$-designs with $(t+1)^2$ points on the unit sphere $S^2$ in $R^3$. We show that the construction of spherical designs is equivalent to solution of underdetermined equations. A new verification method for underdetermined equations is derived using Brouwer’s fixed point theorem. Application of the method provides spherical $t$-designs which are close to extremal (maximum determinant) points and have the optimal order $O(t^2)$ for the number of points. An error bound for the computed spherical designs is provided.