文献类型：期刊文献

英文题名：Smoothness equivalence properties of interpolatory Lie group subdivision schemes

作者：Xie, Gang[2];Yu, Thomas P. -Y.[1]

机构：[1]Drexel Univ, Dept Math, Korman Ctr 206, Philadelphia, PA 19104 USA;[2]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2010

卷号：30

期号：3

起止页码：731

外文期刊名：IMA JOURNAL OF NUMERICAL ANALYSIS

收录：;EI(收录号：20214911269595);WOS:【SCI-EXPANDED(收录号:WOS:000280710400006)】；

基金：National Science Foundation (DMS 0512673).

语种：英文

外文关键词：subdivision schemes; Lie groups; matrix Lie groups; interpolation; smoothness equivalence; breakdown of smoothness equivalence

摘要：We prove that any interpolatory Lie group subdivision scheme based on combining a linear interpolatory subdivision scheme (S) over bar with the log-exp adaption to Lie-group-valued data in Ur Rahman et al. (2005, Multiscale Model. Simul., 4, 1201-1232) produces parameterized curves on the Lie group that are as smooth as the smoothness of (S) over bar -no matter how smooth (S) over bar is. We present both an extrinsic proof and an intrinsic proof. We discuss two variations of our main result. (i) We illustrate how smoothness equivalence can break down in a variant of the original log-exp scheme. (ii) We show that the main result of this paper can be easily extended to a multivariate setting.