Simultaneous approximation by spherical neural networks

被引：3

作者：

Lin, Shaobo ^{[1
]}

Cao, Feilong ^{[2
]}

机构：

[1] Wenzhou Univ, Coll Math & Informat Sci, Wenzhou 325035, Peoples R China

[2] China Jiliang Univ, Inst Metrol & Computat Sci, Hangzhou 310018, Zhejiang, Peoples R China

来源：

NEUROCOMPUTING | 2016年 / 175卷

基金：

中国国家自然科学基金;

关键词：

Spherical neural networks; Simultaneous approximation; Laplace-Beltrami operator; Spherical polynomials; JACKSON-TYPE INEQUALITY; ZONAL FUNCTION NETWORKS; RADIAL BASIS FUNCTIONS; SCATTERED DATA; SPHERES; INTERPOLATION; ERROR; TRACTABILITY; DIMENSION; SMOOTH;

D O I：

10.1016/j.neucom.2015.10.067

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Approximation capabilities of the spherical neural networks (SNNs) are considered in this paper. Based on a known Taylor formula, we prove that, for non-polynomial target function, rates of simultaneously approximating the function itself and its (Laplace-Beltrami) derivatives by SNNs is not slower than those by the spherical polynomials (SPs). Then, the simultaneous approximation rates of SPs automatically derive the rates of SNNs. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：348 / 354

页数：7

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