Parametrized hyperbolic tangent based Banach space valued multivariate multi layer neural network approximations

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Keywords:

multi layer approximation, parametrized hyperbolic tangent sigmoid function, multivariate neural network approximation, quasi-interpolation operator, Kantorovich type operator, quadrature type operator, multivariate modulus of continuity, abstract approximation, iterated

Abstract

Here we examine the multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or RN , N ∈ N, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We research also the case of approximation by iterated operators of the last four types, that is multi hidden layer approximations. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fr´echet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by a parametrized hyperbolic tangent sigmoid function. The approximations are pointwise, uniform and Lp. The related feed-forward neural networks are with one or multi hidden layers.

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Published

2023-12-16

How to Cite

George A. Anastassiou, & Seda Karateke. (2023). Parametrized hyperbolic tangent based Banach space valued multivariate multi layer neural network approximations. Journal of Computational Analysis and Applications (JoCAAA), 31(4), 490–519. Retrieved from http://eudoxuspress.com/index.php/pub/article/view/94

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