A globally convergent numerical algorithm for computing the centre of mass on compact Lie groups
作者： J.H. Manton
DOI: 10.1109/ICARCV.2004.1469774
关键词:
摘要: Motivated by applications in fuzzy control, robotics and vision, this paper considers the problem of computing centre mass (precisely, Karcher mean) a set points defined on compact Lie group, such as special orthogonal group consisting all matrices with unit determinant. An iterative algorithm, whose derivation is based geometry problem, proposed. It proved to be globally convergent. Interestingly, proof starts showing algorithm actually Riemannian gradient descent fixed step size.
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