Holonomic gradient descent and its application to the Fisher-Bingham integral

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

Research output: Contribution to journalArticlepeer-review

43 Citations (Scopus)


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 Sn, which is used in the directional statistics. The method utilizes the theory and algorithms of holonomic systems.

Original languageEnglish
Pages (from-to)639-658
Number of pages20
JournalAdvances in Applied Mathematics
Issue number3
Publication statusPublished - 2011 Sept
Externally publishedYes


  • D-modules
  • Directional statistics
  • Fisher-Bingham distribution
  • Gradient descent
  • Gröbner basis
  • Holonomic function
  • Maximum likelihood

ASJC Scopus subject areas

  • Applied Mathematics


Dive into the research topics of 'Holonomic gradient descent and its application to the Fisher-Bingham integral'. Together they form a unique fingerprint.

Cite this