抄録
Geometric structures of a manifold of positive definite Hermite matrices are considered from the viewpoint of information geometry. A Riemannian metric is defined and dual α-connections are introduced. Then the fact that the manifold is ±1-flat is shown. Moreover, the divergence of two points on the manifold is given through dual potential functions. Furthermore, the optimal approximation of a point onto the submanifold is gotten. Finally, some simulations are given to illustrate our results.
| 元の言語 | English |
|---|---|
| ページ（範囲） | 2137-2145 |
| ページ数 | 9 |
| ジャーナル | Acta Mathematica Sinica, English Series |
| 巻 | 30 |
| 発行部数 | 12 |
| DOI | |
| 出版物ステータス | Published - 2014 11 7 |
| 外部発表 | Yes |
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ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
これを引用
The α-geometric structures on manifold of positive definite Hermite matrices. / Duan, Xiao Min; Sun, Hua Fei; Peng, Linyu.
：: Acta Mathematica Sinica, English Series, 巻 30, 番号 12, 07.11.2014, p. 2137-2145.研究成果: Article
}
TY - JOUR
T1 - The α-geometric structures on manifold of positive definite Hermite matrices
AU - Duan, Xiao Min
AU - Sun, Hua Fei
AU - Peng, Linyu
PY - 2014/11/7
Y1 - 2014/11/7
N2 - Geometric structures of a manifold of positive definite Hermite matrices are considered from the viewpoint of information geometry. A Riemannian metric is defined and dual α-connections are introduced. Then the fact that the manifold is ±1-flat is shown. Moreover, the divergence of two points on the manifold is given through dual potential functions. Furthermore, the optimal approximation of a point onto the submanifold is gotten. Finally, some simulations are given to illustrate our results.
AB - Geometric structures of a manifold of positive definite Hermite matrices are considered from the viewpoint of information geometry. A Riemannian metric is defined and dual α-connections are introduced. Then the fact that the manifold is ±1-flat is shown. Moreover, the divergence of two points on the manifold is given through dual potential functions. Furthermore, the optimal approximation of a point onto the submanifold is gotten. Finally, some simulations are given to illustrate our results.
KW - information geometry
KW - optimal approximation
KW - Positive definite Hermite matrices
UR - http://www.scopus.com/inward/record.url?scp=84911463716&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84911463716&partnerID=8YFLogxK
U2 - 10.1007/s10114-014-1285-x
DO - 10.1007/s10114-014-1285-x
M3 - Article
VL - 30
SP - 2137
EP - 2145
JO - Acta Mathematica Sinica, English Series
JF - Acta Mathematica Sinica, English Series
SN - 1439-8516
IS - 12
ER -