Localized Bases for Kernel Spaces on the Unit Sphere
Localized Bases for Kernel Spaces on the Unit Sphere
复制标题
单位球面上核空间的局部化基
DOI：
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发表时间：
2012
影响因子：
2.9
通讯作者：
G. Wright
中科院分区：
文献类型：
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作者：
E. Fuselier;T. Hangelbroek;F. Narcowich;J. Ward;G. Wright
从正定或条件正定核空间的近似/插值是一种越来越流行的工具，用于分析和合成分散的数据，是许多无网格方法的核心。对于一组$N$分散的网站，这样一个空间的标准基础利用$N$全球支持的内核;计算与它是昂贵的大$N$。易于计算，定位良好的基础与“小足迹”的基础元素-即，仅使用少量内核的元素-已经不可用。在$\mathbb{S}^2$上工作，重点是限制曲面样条核（例如，薄板样条限制到球），我们构造容易计算的，空间局部化，小足迹，强大的基础相关联的核空间。我们的理论预测，局部基的每个元素都是通过仅使用$\mathcal{O}（（\log N）^2）$内核的组合来构造的，这使得构造在计算上很便宜。我们证明...
Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data and is central to many meshless methods. For a set of $N$ scattered sites, the standard basis for such a space utilizes $N$ globally supported kernels; computing with it is prohibitively expensive for large $N$. Easily computable, well-localized bases with “small-footprint” basis elements---i.e., elements using only a small number of kernels---have been unavailable. Working on $\mathbb{S}^2$, with focus on the restricted surface spline kernels (e.g., the thin-plate splines restricted to the sphere), we construct easily computable, spatially well-localized, small-footprint, robust bases for the associated kernel spaces. Our theory predicts that each element of the local basis is constructed by using a combination of only $\mathcal{O}((\log N)^2)$ kernels, which makes the construction computationally cheap. We prove that the ...