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Constructive Function
Approximation: Theory and
Practice
D. Docampo
D.R. Hush
C.T. Abdallah
ABSTRACT In this paper we study the theoretical limits of finite con­
structive convex approximations of a given function in a Hilbert space using
elements taken from a reduced subset. We also investigate the trade­o# be­
tween the global error and the partial error during the iterations of the
solution. These results are then specialized to constructive function ap­
proximation using sigmoidal neural networks. The emphasis then shifts to
the implementation issues associated with the problem of achieving given
approximation errors when using a finite number of nodes and a finite data
set for training.
1 Introduction
It has been shown that continuous functions on compact subsets of IR d can
be uniformly approximated by linear combinations of sigmoidal functions

Source: Abdallah, Chaouki T- Electrical and Computer Engineering Department, University of New Mexico

Collections: Engineering