期刊
NEURAL NETWORKS
卷 48, 期 -, 页码 72-77出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.neunet.2013.07.009
关键词
Sigmoidal functions; Multivariate neural networks operators; Uniform approximation; Order of approximation; Lipschitz classes
资金
- GNAMPA
- GNFM of the Italian INdAM
In this paper, we study pointwise and uniform convergence, as well as order of approximation, of a family of linear positive multivariate neural network (NN) operators with sigmoidal activation functions. The order of approximation is studied for functions belonging to suitable Lipschitz classes and using a moment-type approach. The special cases of NN operators, activated by logistic, hyperbolic tangent, and ramp sigmoidal functions are considered. Multivariate NNs approximation finds applications, typically, in neurocomputing processes. Our approach to NN operators allows us to extend previous convergence results and, in some cases, to improve the order of approximation. The case of multivariate quasi-interpolation operators constructed with sigmoidal functions is also considered. (C) 2013 Elsevier Ltd. All rights reserved.
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