TY - JOUR
T1 - Constructive Approximation by Superposition of Sigmoidal Functions
AU - D. Costarelli & R. Spigler
JO - Analysis in Theory and Applications
VL - 2
SP - 169
EP - 196
PY - 2013
DA - 2013/06
SN - 29
DO - http://doi.org/10.4208/ata.2013.v29.n2.8
UR - https://global-sci.org/intro/article_detail/ata/4525.html
KW - Sigmoidal functions, multivariate approximation, $L^p$ approximation, neural networks, radial basis functions.
AB - <p style="text-align: justify;">In this paper, a constructive theory is developed for approximating functions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the $L^p$ norm. Results for the simultaneous approximation, with the same order of accuracy, of a function and its derivatives (whenever these exist), are obtained. The relation with neural networks and radial basis functions approximations is discussed. Numerical examples are given for the purpose of illustration.</p>