Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting

In: Mathematica Slovaca, vol. 67, no. 6

Danilo Costarelli - Gianluca Vinti

Detaily:

Rok, strany: 2017, 1469 - 1480

Kľúčové slová:

sigmoidal functions, neural networks operators, uniform approximation, $L^p$-approximation, max-product operators

DOI: https://doi.org/10.1515/ms-2017-0063

O článku:

The theory of multivariate neural network operators in a Kantorovich type version is here introduced and studied. The main results concerns the approximation of multivariate data, with respect to the uniform and $L^p$ norms, for continuous and $L^p$ functions, respectively. The above family of operators, are based upon kernels generated by sigmoidal functions. Multivariate approximation by constructive neural network algorithms are useful for applications to neurocomputing processes involving high dimensional data. At the end of the paper, several examples of sigmoidal functions for which the above theory holds have been presented.

Ako citovať:

ISO 690:

Costarelli, D., Vinti, G. 2017. Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting. In Mathematica Slovaca, vol. 67, no.6, pp. 1469-1480. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0063

APA:

Costarelli, D., Vinti, G. (2017). Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting. Mathematica Slovaca, 67(6), 1469-1480. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0063

O vydaní:

Publikované: 27. 11. 2017