Katsuyoshi Ohara
Kanazawa University
Network
Latest external collaboration on country level. Dive into details by clicking on the dots.
Publication
Featured researches published by Katsuyoshi Ohara.
Advances in Applied Mathematics | 2011
Hiromasa Nakayama; Kenta Nishiyama; Masayuki Noro; Katsuyoshi Ohara; Tomonari Sei; Nobuki Takayama; Akimichi Takemura
We give a new algorithm to find local maximum and minimum of a holonomic function and apply it for the Fisher-Bingham integral on the sphere
Journal of Multivariate Analysis | 2013
Tomonari Sei; Hiroki Shibata; Akimichi Takemura; Katsuyoshi Ohara; Nobuki Takayama
S^n
international symposium on symbolic and algebraic computation | 2016
Katsusuke Nabeshima; Katsuyoshi Ohara; Shinichi Tajima
, which is used in the directional statistics. The method utilizes the theory and algorithms of holonomic systems.
international congress on mathematical software | 2014
Tamio Koyama; Hiromasa Nakayama; Katsuyoshi Ohara; Tomonari Sei; Nobuki Takayama
We study properties of Fisher distribution (von Mises-Fisher distribution, matrix Langevin distribution) on the rotation group SO(3). In particular we apply the holonomic gradient descent, introduced by Nakayama et al. (2011) [16], and a method of series expansion for evaluating the normalizing constant of the distribution and for computing the maximum likelihood estimate. The rotation group can be identified with the Stiefel manifold of two orthonormal vectors. Therefore from the viewpoint of statistical modeling, it is of interest to compare Fisher distributions on these manifolds. We illustrate the difference with an example of near-earth objects data.
international congress on mathematical software | 2014
Katsuyoshi Ohara; Shinichi Tajima; Akira Terui
An algorithm for computing comprehensive Gröbner systems (CGS) is introduced in rings of linear partial differential operators. Their applications to b-functions are considered. The resulting algorithm designed for a wide use of computing comprehensive Gröbner systems can be used to compute all the roots of b-functions and relevant holonomic D-modules. Furthermore, with our implementation, effective methods are illustrated for computing holonomic D-modules associated with hypersurface singularities. It is shown that the proposed algorithm is full of versatility.
Journal of Symbolic Computation | 2017
Katsusuke Nabeshima; Katsuyoshi Ohara; Shinichi Tajima
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 in- tegrals 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).
International Journal of Mathematics | 2017
Jyoichi Kaneko; Keiji Matsumoto; Katsuyoshi Ohara
We are developing linear algebra packages on Risa/Asir, a computer algebra system. The aim is to provide programs for efficiently and exactly solving eigenproblems on the computer algebra system for large scale square matrices over integers or rational numbers. The software package consists of some programs. The followings are currently prepared for solving eigenproblems: computing eigenspaces, the spectral decomposition, Jordan chains and minimal annihilating polynomials.
international congress on mathematical software | 2014
Shinichi Tajima; Katsuyoshi Ohara; Akira Terui
Abstract A computation method of comprehensive Grobner systems is introduced in Poincare–Birkhoff–Witt (PBW) algebras and applications to Bernstein–Sato ideals, holonomic D-modules for parametric cases are considered. The proposed method provides in particular holonomic D-modules associated with primary components of Bernstein–Sato ideals. Furthermore, with our implementation, effective methods are illustrated for computing b-functions of μ-constant deformations of hypersurface isolated singularities by utilizing holonomic D-modules. High versatility of the proposed method is also illustrated by several examples.
Proceedings of the Fifth Asian Symposium (ASCM 2001) | 2001
Masahide Maekawa; Masayuki Noro; Nobuki Takayama; Yasushi Tamura; Katsuyoshi Ohara
We study a hypergeometric function in two variables and a system of hypergeometric differential equations associated with this function. This is a regular holonomic system of rank
Journal of Pure and Applied Algebra | 2009
Katsuyoshi Ohara; Nobuki Takayama
9