Approximation by series of sigmoidal functions with applications to neural networks
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| 024 | 7 | 0 | |a 10.1007/s10231-013-0378-y |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-013-0378-y | ||
| 245 | 0 | 0 | |a Approximation by series of sigmoidal functions with applications to neural networks |h [Elektronische Daten] |c [Danilo Costarelli, Renato Spigler] |
| 520 | 3 | |a 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. | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2013 | ||
| 690 | 7 | |a Sigmoidal functions |2 nationallicence | |
| 690 | 7 | |a Neural networks approximation |2 nationallicence | |
| 690 | 7 | |a Order of approximation |2 nationallicence | |
| 690 | 7 | |a Truncation error |2 nationallicence | |
| 690 | 7 | |a Multiresolution approximation |2 nationallicence | |
| 690 | 7 | |a Wavelet-scaling functions |2 nationallicence | |
| 700 | 1 | |a Costarelli |D Danilo |u Dipartimento di Matematica e Fisica, Sezione di Matematica, Università "Roma Tre”, 1, Largo S. Leonardo Murialdo, 00146, Rome, Italy |4 aut | |
| 700 | 1 | |a Spigler |D Renato |u Dipartimento di Matematica e Fisica, Sezione di Matematica, Università "Roma Tre”, 1, Largo S. Leonardo Murialdo, 00146, Rome, Italy |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/1(2015-02-01), 289-306 |x 0373-3114 |q 194:1<289 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-013-0378-y |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-013-0378-y |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Costarelli |D Danilo |u Dipartimento di Matematica e Fisica, Sezione di Matematica, Università "Roma Tre”, 1, Largo S. Leonardo Murialdo, 00146, Rome, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Spigler |D Renato |u Dipartimento di Matematica e Fisica, Sezione di Matematica, Università "Roma Tre”, 1, Largo S. Leonardo Murialdo, 00146, Rome, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/1(2015-02-01), 289-306 |x 0373-3114 |q 194:1<289 |1 2015 |2 194 |o 10231 | ||