@Article{ATA-29-169, author = {}, title = {Constructive Approximation by Superposition of Sigmoidal Functions}, journal = {Analysis in Theory and Applications}, year = {2013}, volume = {29}, number = {2}, pages = {169--196}, abstract = {

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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2013.v29.n2.8}, url = {http://global-sci.org/intro/article_detail/ata/4525.html} }