Generalized symmetrical sigmoid function activated neural network multivariate approximation

다국어 초록 (Multilingual Abstract)

Here we exhibit 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 achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fr\'{e}chet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by the generalized symmetrical sigmoid function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer.

참고문헌 (Reference)

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