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

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	348-354
Number of pages	7
Journal	Neurocomputing
Volume	175
Issue number	PartA
DOIs	https://doi.org/10.1016/j.neucom.2015.10.067
State	Published - 22 May 2015
Externally published	Yes

Keywords

Laplace–Beltrami operator
Simultaneous approximation
Spherical neural networks
Spherical polynomials

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10.1016/j.neucom.2015.10.067

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abstract = "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.",

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author = "Shaobo Lin and Feilong Cao",

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AU - Cao, Feilong

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N2 - 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.

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

UR - https://www.scopus.com/pages/publications/84964978162

U2 - 10.1016/j.neucom.2015.10.067

DO - 10.1016/j.neucom.2015.10.067

M3 - 文章

AN - SCOPUS:84964978162

SN - 0925-2312

VL - 175

SP - 348

EP - 354

JO - Neurocomputing

JF - Neurocomputing

IS - PartA

ER -

Simultaneous approximation by spherical neural networks

Abstract

Keywords

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