Opuscula Math. 27, no. 1 (2007), 59-72

 
Opuscula Mathematica

Approximation properties of some two-layer feedforward neural networks

Michał A. Nowak

Abstract. In this article, we present a multivariate two-layer feedforward neural networks that approximate continuous functions defined on \([0,1]^d\). We show that the \(L_1\) error of approximation is asymptotically proportional to the modulus of continuity of the underlying function taken at \(\sqrt{d}/n\), where \(n\) is the number of function values used.

Keywords: neural networks, approximation of functions, sigmoidal function.

Mathematics Subject Classification: 41A35, 41A63, 41A25, 92B20.

Full text (pdf)

  • Michał A. Nowak
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland
  • Received: 2004-05-17.
Opuscula Mathematica - cover

Cite this article as:
Michał A. Nowak, Approximation properties of some two-layer feedforward neural networks, Opuscula Math. 27, no. 1 (2007), 59-72

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.