TY - JOUR T1 - Constructive Approximation by Superposition of Sigmoidal Functions 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 -

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.