A Geodesic-Based Riemannian Gradient Approach to Averaging on the Lorentz Group

作者：Wang, Jing; Sun, Huafei^*; Li, Didong

来源：Entropy, 2017, 19(12): 698.

DOI：10.3390/e19120698

• Lorentz group
• geodesic
• average
• Riemannian-steepest-descent algorithm
• extended Hamiltonian algorithm

In this paper, we propose an efficient algorithm to solve the averaging problem on the Lorentz group O (n,k). Firstly, we introduce the geometric structures of O (n,k) endowed with a Riemannian metric where geodesic could be written in closed form. Then, the algorithm is presented based on the Riemannian-steepest-descent approach. Finally, we compare the above algorithm with the Euclidean gradient algorithm and the extended Hamiltonian algorithm. Numerical experiments show that the geodesic-based Riemannian-steepest-descent algorithm performs the best in terms of the convergence rate.

• 出版日期2017-12
• 单位北京理工大学