Univariate hyperbolic tangent neural network approximation
โ Scribed by George A. Anastassiou
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 299 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0895-7177
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Here we study the multivariate quantitative constructive approximation of real and complex valued continuous multivariate functions on a box or RN, NโN, by the multivariate quasi-interpolation sigmoidal neural network operators. The "right" operators for our goal are fully and precisely described. T
Let D/R d be a compact set and let 8 be a uniformly bounded set of D ร R functions. For a given real-valued function f defined on D and a given natural number n, we are looking for a good uniform approximation to f of the form n i=1 a i , i , with , i # 8, a i # R. Two main cases are considered: (1)
Let D be a set with a probability measure +, +(D)=1, and let K be a compact subset of L q (D, +), where the infimum is taken over all g n of the form g n = n i=1 a i , i , with arbitrary , i # K and a i # R. It is shown that for f # conv(K \_ (&K )), under some mild restrictions, \ n ( f, K ) C q =