Multiscale Analysis in Sobolev Spaces on the Sphere
Multiscale Analysis in Sobolev Spaces on the Sphere
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DOI：
10.1137/090774550
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发表时间：
2010-12
期刊：
影响因子：
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通讯作者：
Q. Gia;I. Sloan;H. Wendland
中科院分区：
文献类型：
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作者：
Q. Gia;I. Sloan;H. Wendland
我们考虑了单位球面$\mathbb{S}^n$上Sobolev空间中函数在离散点处的多尺度逼近方案。近似构造使用一系列的缩放，compounds支持的径向基函数限制为$\mathbb{S}^n$。证明了该方案的收敛性定理，并证明了线性系统的条件数从一级到另一级保持有界，从而首次建立了在离散数据点上用单一紧支径向基函数的尺度形式进行多尺度逼近的数学理论.
We consider a multiscale approximation scheme at scattered sites for functions in Sobolev spaces on the unit sphere $\mathbb{S}^n$. The approximation is constructed using a sequence of scaled, compactly supported radial basis functions restricted to $\mathbb{S}^n$. A convergence theorem for the scheme is proved, and the condition number of the linear system is shown to stay bounded by a constant from level to level, thereby establishing for the first time a mathematical theory for multiscale approximation with scaled versions of a single compactly supported radial basis function at scattered data points.