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Multivariate sigmoidal neural network approximation
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DOI：10.1016/j.neunet.2011.01.003.png)
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Here we study the multivariate quantitative constructive approximation of real and complex valued continuous multivariate functions on a box or R(N), N epsilon N, by the multivariate quasi-interpolation sigmoidal neural network operators. The right operators for our goal are fully and precisely described. This approximation is derived by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order partial derivatives. Our multivariate operators are defined by using a multidimensional density function induced by the logarithmic sigmoidal function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer. (C) 2011 Elsevier Ltd. All rights reserved.
Keyword:
Sigmoidal function
Multivariate neural network approximation
Multivariate quasi-interpolation operator
Multivariate modulus of continuiuty
Complex approximation
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