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A list of references for HGM is put on the web.

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<h1> References for the Holonomic Gradient Method (HGM) and
the Holonomic Gradient Descent Method  (HGD) </h1>

<h2> Papers  and Tutorials</h2>
<ol>
<li> T.Koyama,
Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,
<a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>

<li> T.Hibi, K.Nishiyama, N.Takayama,
Pfaffian Systems of A-Hypergeometric Equations I,
Bases of Twisted Cohomology Groups,
<a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
(major revision v2 of arxiv:1212.6103)

<li> <img src="./wakaba01.png" alt="Intro">
<a href="http://link.springer.com/book/10.1007/978-4-431-54574-3"> 
T.Hibi et al, Groebner Bases : Statistics and Software Systems </a>, Springer, 2013.

<li> <img src="./wakaba01.png" alt="Intro">
Introduction to the Holonomic Gradient Method (movie), 2013. 
<a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>

<li> T.Sei, A.Kume,
Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method,
Statistics and Computing, 2013,
<a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>

<li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
Holonomic Rank of the Fisher-Bingham System of Differential Equations,
<!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
to appear in Journal of Pure and Applied Algebra

<li>
T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
<!-- <a href="http://arxiv.org/abs/1201.3239"> 1201.3239 </a> -->
Computational Statistics (2013)
<a href="http://dx.doi.org/10.1007/s00180-013-0456-z"> DOI </a>

<li> Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
<!-- <a href="http://arxiv.org/abs/1201.0472"> 1201.0472 </a> -->
Journal of Multivariate Analysis, 117, (2013) 296-312,
<a href="http://dx.doi.org/10.1016/j.jmva.2013.03.011"> DOI </a> 

<li> Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama,
Properties and applications of Fisher distribution on the rotation group,
<!-- <a href="http://arxiv.org/abs/1110.0721"> 1110.0721 </a> -->
Journal of Multivariate Analysis, 116 (2013), 440--455,
<a href="http://dx.doi.org/10.1016/j.jmva.2013.01.010">DOI</a>

<li>T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral,
Funkcialaj Ekvacioj 56 (2013), 51--61.
<!-- <a href="http://dx.doi.org/10.1619/fesi.56.51">DOI</a> -->
<a href="https://www.jstage.jst.go.jp/article/fesi/56/1/56_51/_article">jstage</a>

<li>
Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
Tomonari Sei, Nobuki Takayama, Akimichi Takemura ,
Holonomic Gradient Descent  and its Application to Fisher-Bingham Integral,
<!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a>  -->
Advances in Applied Mathematics 47 (2011), 639--658,
<a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
</ol>

<h2> Software Packages for HGM</h2>
<ol>
<li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/hgm/"> hgm package for R </a>
<li> yang (for Pfaffian systems) , nk_restriction (for D-module integrations), 
tk_jack  (for Jack polynomials) are in the 
<a href="http://www.math.kobe-u.ac.jp/Asir"> asir-contrib </a>
</ol>

<h2> Programs to try examples of our papers </h2>
<ol>
<li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
</ol>

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