Convergence and smoothness analysis of subdivision rules in Riemannian and symmetric spaces
Convergence and smoothness analysis of subdivision rules in Riemannian and symmetric spaces
复制标题
黎曼空间和对称空间中细分规则的收敛性和平滑性分析
DOI：
10.1007/s10444-010-9150-7
复制
发表时间：
2011
影响因子：
1.7
通讯作者：
A. Weinmann
中科院分区：
文献类型：
--
作者：
J. Wallner;Esfandiar Nava Yazdani;A. Weinmann
在讨论了不变细分规则的可定义性之后，我们讨论了黎曼流形和对称空间中的序列数据的规则，并将正定矩阵空间作为一个主要例子。我们证明了Cartan-Hadamard流形中用内在平均定义的细分规则对所有输入数据收敛，这比通常用于流形细分规则的结果强得多。我们还显示较弱的收敛结果，这是真实的，但只适用于足够密集的输入数据。最后讨论了极限曲线的C1和C2光滑性。
After a discussion on definability of invariant subdivision rules we discuss rules for sequential data living in Riemannian manifolds and in symmetric spaces, having in mind the space of positive definite matrices as a major example. We show that subdivision rules defined with intrinsic means in Cartan-Hadamard manifolds converge for all input data, which is a much stronger result than those usually available for manifold subdivision rules. We also show weaker convergence results which are true in general but apply only to dense enough input data. Finally we discuss C1 and C2 smoothness of limit curves.