A Fast Algorithm for the Moments of Bingham Distribution
Provides a faster, accurate method for computing Bingham moments, benefiting researchers in directional statistics and liquid crystal modeling.
The paper proposes a fast algorithm for evaluating moments of the Bingham distribution, achieving maximal absolute error less than 5e-8 faster than adaptive quadrature, and applies it to a liquid crystal model revealing a different defect pattern from Landau-de Gennes theory.
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.