Riemannian means on special euclidean group and unipotent matrices group

Xiaomin Duan, Huafei Sun*, Linyu Peng

*この研究の対応する著者

研究成果: Article査読

12 被引用数 (Scopus)

抄録

Among the noncompact matrix Lie groups, the special Euclidean group and the unipotent matrix group play important roles in both theoretic and applied studies. The Riemannian means of a finite set of the given points on the two matrix groups are investigated, respectively. Based on the left invariant metric on the matrix Lie groups, the geodesic between any two points is gotten. And the sum of the geodesic distances is taken as the cost function, whose minimizer is the Riemannian mean. Moreover, a Riemannian gradient algorithm for computing the Riemannian mean on the special Euclidean group and an iterative formula for that on the unipotent matrix group are proposed, respectively. Finally, several numerical simulations in the 3-dimensional case are given to illustrate our results.

本文言語English
論文番号292787
ジャーナルThe Scientific World Journal
2013
DOI
出版ステータスPublished - 2013
外部発表はい

ASJC Scopus subject areas

  • 生化学、遺伝学、分子生物学(全般)
  • 環境科学(全般)
  • 医学(全般)

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