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A Fast Algorithm for the Moments of Bingham Distribution

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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 tests show that the algorithm reaches the maximum absolute error less than \(5\times 10^{-8}\) 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.

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  1. https://github.com/yixiangLuo/Bingham-moment-function/.

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA

    Yixiang Luo

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Jie Xu

  3. LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Pingwen Zhang

Authors
  1. Yixiang Luo
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  2. Jie Xu
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  3. Pingwen Zhang
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Corresponding author

Correspondence to Jie Xu.

Additional information

Pingwen Zhang is supported by National Natural Science Foundations of China (Grant Nos. 11421101 and 11421110001).

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Luo, Y., Xu, J. & Zhang, P. A Fast Algorithm for the Moments of Bingham Distribution. J Sci Comput 75, 1337–1350 (2018). https://doi.org/10.1007/s10915-017-0589-2

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  • DOI: https://doi.org/10.1007/s10915-017-0589-2

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