Holonomic Gradient Descent and its Application to Fisher-Bingham Integral

Authors :: Sei, Tomonari
Takayama, Nobuki
Takemura, Akimichi
Nakayama, Hiromasa
Nishiyama, Kenta
Noro, Masayuki
Ohara, Katsuyoshi
Source :: Advances in Applied Mathematics 47 (2011) 639-658
Publication Year :: 2010
Abstract: 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.<br />Comment: 23 pages, 1 figure