A Constructive Proof and An Extension of Cybenko’s Approximation Theorem

Tianping Chen, Hong Chen and Ruey-wen Liu
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Tianping Chen: Fudan University, Dept. of Mathematics
Hong Chen: University of Notre Dame, Dept. of Electrical Engineering
Ruey-wen Liu: University of Notre Dame, Dept. of Electrical Engineering

A chapter in Computing Science and Statistics, 1992, pp 163-168 from Springer

Abstract: Abstract In this paper, we present a constructive proof of approximation by superposition of sigmoidal functions. We point out a sufficient condition that the set of finite linear combinations of the form $$\sum \alpha _j\sigma (y_jx+\theta _j)$$ is dense in $$C(\mathbb{I}^n)$$ , is the boundedness of the sigmoidal function σ(x). Moreover, we show that if the set of finite linear combinations of the form $$\sum c_j\omega (\xi _j+\eta _j)$$ , where ω is a univariate function, is dense in $$L^p[a,b] (1\leq p

Keywords: Constructive approximation; Neural networks; Sigmoidal functions (search for similar items in EconPapers)
Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2856-1_21

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DOI: 10.1007/978-1-4612-2856-1_21

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