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

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• 作者：Shihui YingAuthor Vitae ; Han QinAuthor Vitae ; Yaxin PengAuthor Vitae ; Zhijie Wen ; ^{wenzhijie@shu.edu.cn" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：Karcher mean ; Rotation group ; Conjugate gradient method ; Structure preserving
• 刊名：Neurocomputing
• 出版年：2016
• 出版时间：26 November 2016
• 年：2016
• 卷：215
• 期：Complete
• 页码：169-174
• 全文大小：801 K

文摘

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.