General multivariate arctangent function activated neural network approximations

Here we expose multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or \(\mathbb{R}^{N}\), \(N\in \mathbb{N}\), by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the...

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Vydané v:	Journal of numerical analysis and approximation theory Ročník 51; číslo 1; s. 37 - 66
Hlavný autor:	Anastassiou, George A.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Publishing House of the Romanian Academy 17.09.2022
Predmet:	arctangent function Kantorovich type operator multivariate modulus of continuity multivariate neural network approximation quadrature type operator quasi-interpolation operator
ISSN:	2457-6794, 2501-059X
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Popis
Shrnutí:	Here we expose multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or \(\mathbb{R}^{N}\), \(N\in \mathbb{N}\), by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are derived by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Frechet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by the arctangent function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer.
ISSN:	2457-6794 2501-059X
DOI:	10.33993/jnaat511-1262