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

In: Computing Science and Statistics

Author

Listed:
  • 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)

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

Suggested Citation

  • Tianping Chen & Hong Chen & Ruey-wen Liu, 1992. "A Constructive Proof and An Extension of Cybenko’s Approximation Theorem," Springer Books, in: Connie Page & Raoul LePage (ed.), Computing Science and Statistics, pages 163-168, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2856-1_21
    DOI: 10.1007/978-1-4612-2856-1_21
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