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

2019/04/16 by Xiao, Yuchen, An, Congpei · 1 citation
#65D99 #65F99 #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1904.07638

Abstract

A point set \mathrm 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 \mathrm X_N is a stationary point set of A_N,t+1 and the minimal singular value of basis matrix is positive, then \mathrm 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 t+1 up to 127 at N=(t+2)².

Cited by

• On Convergence of Regularized Barzilai-Borwein Method

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