Holonomic Gradient Descent and its Application to Fisher-Bingham Integral

Akimichi Takemura; Hiromasa Nakayama; Katsuyoshi Ohara; Kenta Nishiyama; Masayuki Noro; Nobuki Takayama; Tomonari Sei

arxiv: 1005.5273 · v2 · pith:R4L4CEE5new · submitted 2010-05-28 · 💻 cs.SC · math.OC· math.ST· stat.TH

Holonomic Gradient Descent and its Application to Fisher-Bingham Integral

Tomonari Sei , Nobuki Takayama , Akimichi Takemura , Hiromasa Nakayama , Kenta Nishiyama , Masayuki Noro , Katsuyoshi Ohara This is my paper

classification 💻 cs.SC math.OCmath.STstat.TH

keywords holonomicfisher-binghamintegralalgorithmalgorithmsapplicationapplydescent

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We give a new algorithm to find local maximum and minimum of a holonomic function and apply it for the Fisher-Bingham integral on the sphere $S^n$, which is used in the directional statistics. The method utilizes the theory and algorithms of holonomic systems.

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Holonomic Gradient Descent and its Application to Fisher-Bingham Integral

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