期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 48, 期 6, 页码 2065-2090出版社
SIAM PUBLICATIONS
DOI: 10.1137/090774550
关键词
multiscale; approximation; interpolation; radial basis functions; unit sphere
资金
- Australian Research Council
We consider a multiscale approximation scheme at scattered sites for functions in Sobolev spaces on the unit sphere S-n. The approximation is constructed using a sequence of scaled, compactly supported radial basis functions restricted to 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.
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