caa a22 4500 605495998 CHVBK 20210128100534.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10231-013-0378-y doi (NATIONALLICENCE)springer-10.1007/s10231-013-0378-y Approximation by series of sigmoidal functions with applications to neural networks [Elektronische Daten] [Danilo Costarelli, Renato Spigler] In this paper, we develop a constructive theory for approximating absolutely continuous functions by series of certain sigmoidal functions. Estimates for the approximation error are also derived. The relation with neural networks approximation is discussed. The connection between sigmoidal functions and the scaling functions of $$r$$ r -regular multiresolution approximations are investigated. In this setting, we show that the approximation error for $$C^1$$ C 1 -functions decreases as $$2^{-j}$$ 2 - j , as $$j \rightarrow + \infty $$ j → + ∞ . Examples with sigmoidal functions of several kinds, such as logistic, hyperbolic tangent, and Gompertz functions, are given. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2013 Sigmoidal functions nationallicence Neural networks approximation nationallicence Order of approximation nationallicence Truncation error nationallicence Multiresolution approximation nationallicence Wavelet-scaling functions nationallicence Costarelli Danilo Dipartimento di Matematica e Fisica, Sezione di Matematica, Università "Roma Tre”, 1, Largo S. Leonardo Murialdo, 00146, Rome, Italy aut Spigler Renato Dipartimento di Matematica e Fisica, Sezione di Matematica, Università "Roma Tre”, 1, Largo S. Leonardo Murialdo, 00146, Rome, Italy aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/1(2015-02-01), 289-306 0373-3114 194:1<289 2015 194 10231 https://doi.org/10.1007/s10231-013-0378-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-013-0378-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Costarelli Danilo Dipartimento di Matematica e Fisica, Sezione di Matematica, Università "Roma Tre”, 1, Largo S. Leonardo Murialdo, 00146, Rome, Italy aut NATIONALLICENCE 700 1- Spigler Renato Dipartimento di Matematica e Fisica, Sezione di Matematica, Università "Roma Tre”, 1, Largo S. Leonardo Murialdo, 00146, Rome, Italy aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/1(2015-02-01), 289-306 0373-3114 194:1<289 2015 194 10231