Advances in Computational Mathematics

, Volume 1, Issue 1, pp 61–80 | Cite as

Approximation properties of a multilayered feedforward artificial neural network

  • H. N. Mhaskar


We prove that an artificial neural network with multiple hidden layers and akth-order sigmoidal response function can be used to approximate any continuous function on any compact subset of a Euclidean space so as to achieve the Jackson rate of approximation. Moreover, if the function to be approximated has an analytic extension, then a nearly geometric rate of approximation can be achieved. We also discuss the problem of approximation of a compact subset of a Euclidean space with such networks with a classical sigmoidal response function.


Neural networks uniform approximation multivariate splines analytic functions modulus of smoothness 

Subject classification

(AMS) 41A15 41A63 


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Copyright information

© J.C. Baltzer AG, Science Publishers 1993

Authors and Affiliations

  • H. N. Mhaskar
    • 1
  1. 1.Department of MathematicsCalifornia State UniversityLos AngelesUSA

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