Stability results for approximation by positive definite functions on SO(3)

JOURNAL OF APPROXIMATION THEORY

卷:153

Article

Filbir, Frank¹  Schmid, Dominik¹ 

[1] German Res Ctr Environm Hlth, Helmholtz Zentrum Munchen, Inst Biomath & Biometry, D-85764 Neuherberg, Germany

关键词: scattered data approximation;    rotation group;    positive definite functions;    stability;   

DOI  :  10.1016/j.jat.2008.01.006

来源: Elsevier

【 摘 要 】

We consider interpolation methods defined by positive definite functions on a locally compact group G. Estimates for the smallest and largest eigenvalue of the interpolation matrix in terms of the localization of the positive definite function on G are presented, and we provide a method to get positive definite functions explicitly on compact semisimple Lie groups. Finally, we apply our results to construct well-localized positive definite basis functions having nice stability properties on the rotation group SO(3). (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free