Skip Navigation



IMA Journal of Numerical Analysis Advance Access published online on July 4, 2008
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drn033
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Shingel, T.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Interpolation in special orthogonal groups

Tatiana Shingel{dagger}

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, UK

{dagger} Email: t.shingel{at}damtp.cam.ac.uk

Received on 8 August 2007. Accepted for publication 17 April 2008.


  Abstract

In this paper, we propose a scheme to generate interpolating curves in Lie groups, focusing on a special orthogonal group SO(n) due to its practical importance. Our technique is based on the exponential representation of the elements of the group, which allows as to transfer the problem to the corresponding Lie algebra s(n) and benefit from the linearity of this space. Due to the exponential representation, we can obtain a high degree of smoothness of an interpolating curve. The underlying problem is challenging because the standard SO(n) —-> s(n) map is multivalued.

Key Words: interpolation; Lie groups; special orthogonal group


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.