MULTISCALE ANALYSIS IN SOBOLEV SPACES ON THE SPHERE

被引：57

作者：

Le Gia, Q. T. ^{[1
]}

Sloan, I. H. ^{[1
]}

Wendland, H. ^{[2
]}

机构：

[1] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

[2] Univ Oxford, Math Inst, Oxford OX1 3LB, England

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2010年 / 48卷 / 06期

基金：

澳大利亚研究理事会;

关键词：

multiscale; approximation; interpolation; radial basis functions; unit sphere; SCATTERED DATA INTERPOLATION; RADIAL BASIS FUNCTIONS; APPROXIMATION;

D O I：

10.1137/090774550

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：2065 / 2090

页数：26

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