Compute Karcher means on SO(n) by the geometric conjugate gradient method

In this paper, numerical methods to compute the Karcher means on the n-order rotation group SO(n) are considered. First, after recalling Karcher means as solutions of a kind of minimization problems on SO(n), a super-linearly convergent numerical method, namely conjugate gradient method, has been used to deal with them. By the geometric structure of SO(n), the proposed algorithm is structure preserving. Then, a variety of numerical experiments are presented to demonstrate the performance and efficiency of the proposed algorithm by comparing with a recent structure preserving method.