Details:
Title  Holonomic gradient descent and its application to the Fisher–Bingham integral  Author(s)  Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, Tomonari Sei, Nobuki Takayama, Akimichi Takemura  Type  Article in Journal  Abstract  We give a new algorithm to find local maxima and minima 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.  Keywords  Holonomic function, Maximum likelihood, Gradient descent, Directional statistics, Dmodules, Gröbner basis, Fisher–Bingham distribution  ISSN  01968858 
URL 
http://www.sciencedirect.com/science/article/pii/S019688581100008X 
Language  English  Journal  Advances in Applied Mathematics  Volume  47  Number  3  Pages  639  658  Year  2011  Edition  0  Translation 
No  Refereed 
No 
