Constructive Approximation by Superposition of Sigmoidal Functions

被引：2

作者：

Danilo Costarelli ^{[1
]}

Renato Spigler ^{[1
]}

机构：

[1] Dipartimento di Matematica, Universita` "Roma Tre", 1, Largo S. Leonardo Murialdo, 00146 Rome, Italy

来源：

AnalysisinTheoryandApplications | 2013年 / 29卷 / 02期

关键词：

Sigmoidal functions; multivariate approximation; L p approximation; neural net- works; radial basis functions;

D O I：

暂无

中图分类号：

O174 [函数论];

学科分类号：

070104 ;

摘要：

In this paper, a constructive theory is developed for approximating functions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L p norm. Results for the simultaneous approximation, with the same order of accuracy, of a function and its derivatives (whenever these exist), are obtained. The relation with neural networks and radial basis functions approximations is discussed. Numerical examples are given for the purpose of illustration.

引用

页码：169 / 196

页数：28

共 50 条

[21] Approximation of the Heaviside function by sigmoidal functions in reaction-diffusion equations
Sun, Wenlong
Han, Xiaoying
Kloeden, Peter E.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2024, 128
[22] Construction and approximation rate for feedforward neural network operators with sigmoidal functions
Yu, Dansheng
Cao, Feilong
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2025, 453
[23] On sigmoidal functions
Medvedeva, MV
VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA, 1998, (01): : 16 - 20
[24] Constructive Approximation of Continuous Interval-Valued Functions
Font, Juan J.
Macario, Sergio
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2022, 43 (02) : 127 - 144
[25] An analog of the Jackson-Nikol'skii theorem on the approximation by superpositions of sigmoidal functions
Andrianov, AV
MATHEMATICAL NOTES, 1996, 59 (5-6) : 661 - 664
[26] On the approximation capability of neural networks using bell-shaped and sigmoidal functions
Ciuca, I
1998 IEEE INTERNATIONAL CONFERENCE ON SYSTEMS, MAN, AND CYBERNETICS, VOLS 1-5, 1998, : 1845 - 1850
[27] Solving numerically nonlinear systems of balance laws by multivariate sigmoidal functions approximation
Danilo Costarelli
Renato Spigler
Computational and Applied Mathematics, 2018, 37 : 99 - 133
[28] Solving numerically nonlinear systems of balance laws by multivariate sigmoidal functions approximation
Costarelli, Danilo
Spigler, Renato
COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (01): : 99 - 133
[29] Constructive methods of approximation of entire functions of exponential type with the use of atomic functions
Basarab, M.A.
Kravchenko, V.F.
2002, Begell House Inc. (58): : 9 - 10
[30] Approximation by superpositions of a sigmoidal function
Lewicki, G
Marino, G
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2003, 22 (02): : 463 - 470

← 1 2 3 4 5 →