TY - JOUR
A2 - Abu-Saris, R.
A2 - Bracken, P.
AU - Duan, Xiaomin
AU - Sun, Huafei
AU - Peng, Linyu
PY - 2013
DA - 2013/10/24
TI - Riemannian Means on Special Euclidean Group and Unipotent Matrices Group
SP - 292787
VL - 2013
AB - 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.
SN - 2356-6140
UR - https://doi.org/10.1155/2013/292787
DO - 10.1155/2013/292787
JF - The Scientific World Journal
PB - Hindawi Publishing Corporation
KW -
ER -