Riemannian means on special euclidean group and unipotent matrices group

Xiaomin Duan, Huafei Sun, Linyu Peng

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number292787
JournalThe Scientific World Journal
Volume2013
DOIs
Publication statusPublished - 2013
Externally publishedYes

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Costs and Cost Analysis
matrix
Lie groups
Cost functions
Computer simulation
cost
simulation

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Medicine(all)

Cite this

Riemannian means on special euclidean group and unipotent matrices group. / Duan, Xiaomin; Sun, Huafei; Peng, Linyu.

In: The Scientific World Journal, Vol. 2013, 292787, 2013.

Research output: Contribution to journalArticle

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