Simultaneous approximation by spherical neural networks

Shaobo Lin; Feilong Cao

doi:10.1016/j.neucom.2015.10.067

Simultaneous approximation by spherical neural networks

Shaobo Lin
, Feilong Cao

Wenzhou University
China Jiliang University

科研成果: 期刊稿件 › 文章 › 同行评审

13 引用（Scopus）

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.

源语言	英语
页（从-至）	348-354
页数	7
期刊	Neurocomputing
卷	175
期	PartA
DOI	https://doi.org/10.1016/j.neucom.2015.10.067
出版状态	已出版 - 22 5月 2015
已对外发布	是

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keywords = "Laplace{\textendash}Beltrami operator, Simultaneous approximation, Spherical neural networks, Spherical polynomials",

author = "Shaobo Lin and Feilong Cao",

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AU - Cao, Feilong

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AB - 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.

KW - Laplace–Beltrami operator

KW - Simultaneous approximation

KW - Spherical neural networks

KW - Spherical polynomials

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ER -

Simultaneous approximation by spherical neural networks

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