A Fast Algorithm for the Moments of Bingham Distribution

Abstract

We propose a fast algorithm for evaluating the moments of Bingham distribution. The calculation is done by piecewise rational approximation, where interpolation and Gaussian integrals are utilized. Numerical test shows that the algorithm reaches the maximal absolute error less than 5e-8 remarkably faster than adaptive numerical quadrature. We apply the algorithm to a model for liquid crystals with the Bingham distribution to examine the defect patterns of rod-like molecules confined in a sphere, and find a different pattern from the Landau-de Gennes theory.