APPROXIMATION BY POSITIVE DEFINITE FUNCTIONS ON COMPACT GROUPS

被引：7

作者：

Erb, Wolfgang ^{[2
]}

Filbir, Frank ^{[1
]}

机构：

[1] GSF Res Ctr, Inst Biomath & Biometry, D-85764 Neuherberg, Germany

[2] Tech Univ Munich, Ctr Math Sci, D-8046 Garching, Germany

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2008年 / 29卷 / 9-10期

关键词：

Positive definite functions; Rotation group; Scattered data approximation;

D O I：

10.1080/01630560802484310

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider approximation methods defined by translates of a positive definite function on a compact group. A characterization of the native space generated by a positive definite function on a compact group is presented. Starting from Bochner's theorem, we construct examples of well-localized positive definite central functions on the rotation group SO(3). Finally, the stability of the interpolation problem and the error analysis for the given examples are studied in detail.

引用

页码：1082 / 1107

页数：26

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