Software Packages for Holonomic Gradient Method

  • Tamio Koyama
  • Hiromasa Nakayama
  • Katsuyoshi Ohara
  • Tomonari Sei
  • Nobuki Takayama
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8592)

Abstract

We present software packages for the holonomic gradient method (HGM). These packages compute normalizing constants and the probabilities of some regions. While many algorithms which compute integrals over high-dimensional regions utilize the Monte-Carlo method, our HGM utilizes algorithms for solving ordinary differential equations such as the Runge-Kutta-Fehlberg method. As a result, our HGM can evaluate many integrals with a high degree of accuracy and moderate computational time. The source code of our packages is distributed on our web page [12].

Keywords

holonomic gradient method normalizing constant region probability Bingham prior R project 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Tamio Koyama
    • 1
  • Hiromasa Nakayama
    • 2
  • Katsuyoshi Ohara
    • 3
  • Tomonari Sei
    • 4
  • Nobuki Takayama
    • 5
  1. 1.Department of Mathematical Informatics, Graduate School of Information Science and TechnologyUniversity of Tokyo, JSPS Research FellowJapan
  2. 2.Department of MathematicsTokai UniversityJapan
  3. 3.Faculty of Mathematics and PhysicsKanazawa UniversityJapan
  4. 4.Department of MathematicsKeio UniversityJapan
  5. 5.Department of MathematicsKobe UniversityJapan

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