Software packages for holonomic gradient method

Tamio Koyama; Hiromasa Nakayama; Katsuyoshi Ohara; Tomonari Sei; Nobuki Takayama

doi:10.1007/978-3-662-44199-2_105

Software packages for holonomic gradient method

Tamio Koyama, Hiromasa Nakayama, Katsuyoshi Ohara, Tomonari Sei, Nobuki Takayama

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Citations (Scopus)

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].

Original language	English
Title of host publication	Mathematical Software, ICMS 2014 - 4th International Congress, Proceedings
Publisher	Springer Verlag
Pages	706-712
Number of pages	7
ISBN (Print)	9783662441985
DOIs	https://doi.org/10.1007/978-3-662-44199-2_105
Publication status	Published - 2014
Event	4th International Congress on Mathematical Software, ICMS 2014 - Seoul, Korea, Republic of Duration: 2014 Aug 5 → 2014 Aug 9

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8592 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	4th International Congress on Mathematical Software, ICMS 2014
Country/Territory	Korea, Republic of
City	Seoul
Period	14/8/5 → 14/8/9

Keywords

Bingham prior
R project
holonomic gradient method
normalizing constant
region probability

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-662-44199-2_105

Cite this

Koyama, T., Nakayama, H., Ohara, K., Sei, T., & Takayama, N. (2014). Software packages for holonomic gradient method. In Mathematical Software, ICMS 2014 - 4th International Congress, Proceedings (pp. 706-712). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8592 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-662-44199-2_105

Software packages for holonomic gradient method. / Koyama, Tamio; Nakayama, Hiromasa; Ohara, Katsuyoshi et al.
Mathematical Software, ICMS 2014 - 4th International Congress, Proceedings. Springer Verlag, 2014. p. 706-712 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8592 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Koyama, T, Nakayama, H, Ohara, K, Sei, T & Takayama, N 2014, Software packages for holonomic gradient method. in Mathematical Software, ICMS 2014 - 4th International Congress, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8592 LNCS, Springer Verlag, pp. 706-712, 4th International Congress on Mathematical Software, ICMS 2014, Seoul, Korea, Republic of, 14/8/5. https://doi.org/10.1007/978-3-662-44199-2_105

Koyama T, Nakayama H, Ohara K, Sei T, Takayama N. Software packages for holonomic gradient method. In Mathematical Software, ICMS 2014 - 4th International Congress, Proceedings. Springer Verlag. 2014. p. 706-712. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-44199-2_105

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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].",

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Software packages for holonomic gradient method

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