Numerical construction of spherical t-designs by Barzilai-Borwein method

摘要

A point set X_N on the unit sphere is a spherical t-design is equivalent to the nonnegative quantity A_(N,t+1) vanished. We show that if X_N is a stationary point set of A_(N,t+1) and the minimal singular value of basis matrix is positive, then X_N is a spherical t-design. Moreover, the numerical construction of spherical t-designs is valid by using Barzilai-Borwein method. We obtain numerical spherical t-designs with N = (t + 2)~2 points for t + 1 up to 127.