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International Congress on Mathematical Software

ICMS 2014: Mathematical Software – ICMS 2014 pp 706–712Cite as

Software Packages for Holonomic Gradient Method

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Part of the Lecture Notes in Computer Science book series (LNTCS,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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  • DOI: 10.1007/978-3-662-44199-2_105
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References

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  3. Koyama, T., Takemura, A.: Calculation of Orthant Probabilities by the Holonomic Gradient Method, arxiv:1211.6822

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Author information

Authors and Affiliations

  1. Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, JSPS Research Fellow, Japan

    Tamio Koyama

  2. Department of Mathematics, Tokai University, Japan

    Hiromasa Nakayama

  3. Faculty of Mathematics and Physics, Kanazawa University, Japan

    Katsuyoshi Ohara

  4. Department of Mathematics, Keio University, Japan

    Tomonari Sei

  5. Department of Mathematics, Kobe University, Japan

    Nobuki Takayama

Authors
  1. Tamio Koyama
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  2. Hiromasa Nakayama
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  3. Katsuyoshi Ohara
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  4. Tomonari Sei
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  5. Nobuki Takayama
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Editor information

Editors and Affiliations

  1. Department of Mathematics, North Carolina State University, Box 8205, 27695, Raleigh, NC, USA

    Hoon Hong

  2. Courant Institute, Dept. of Computer Science, New York Institute, 251 Mercer Street, 10012, New York, NY, USA

    Chee Yap

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Koyama, T., Nakayama, H., Ohara, K., Sei, T., Takayama, N. (2014). Software Packages for Holonomic Gradient Method. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_105

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  • DOI: https://doi.org/10.1007/978-3-662-44199-2_105

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44198-5

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