Radial kernels via scale derivatives

被引：3

作者：

Bozzini, Mira ^{[1
]}

Rossini, Milvia ^{[1
]}

Schaback, Robert ^{[2
]}

Volonte, Elena ^{[1
]}

机构：

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy

[2] Univ Gottingen, Inst Numer & Angew Math, Fak Math & Informat, D-37073 Gottingen, Germany

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 2015年 / 41卷 / 02期

关键词：

Kernels; Radial basis functions; Scattered data; Meshfree methods; MIXTURES;

D O I：

10.1007/s10444-014-9366-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We generate various new radial kernels by taking derivatives of known kernels with respect to scale. This is different from the well-known scale mixtures used before. In addition, we provide a simple recipe that explicitly constructs new kernels from the negative Laplacian of known kernels. Surprisingly, these two methods for generating new kernels can be proven to coincide for certain standard classes of radial kernels. The resulting radial kernels are positive definite, and a few illustrations are provided.

引用

页码：277 / 291

页数：15

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