Voronovskaja Type Theorems and High-Order Convergence Neural Network Operators with Sigmoidal Functions

Voronovskaja Type Theorems and High-Order Convergence Neural Network Operators with Sigmoidal Functions

In the present paper, asymptotic expansion and Voronovskaja type theorem for the neural network operators have been proved. The above results are based on the computation of the algebraic truncated moments of the density functions generated by suitable sigmoidal functions, such as the logistic funct...

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Veröffentlicht in:Mediterranean journal of mathematics 2020-06, Vol.17 (3), Article 77
Hauptverfasser: Costarelli, Danilo, Vinti, Gianluca
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Asymptotic series
Convergence
Goats
Mathematics
Mathematics and Statistics
Neural networks
Operators
Spline functions
Theorems
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description In the present paper, asymptotic expansion and Voronovskaja type theorem for the neural network operators have been proved. The above results are based on the computation of the algebraic truncated moments of the density functions generated by suitable sigmoidal functions, such as the logistic functions, sigmoidal functions generated by splines and other. Further, operators with high-order convergence are also studied by considering finite linear combination of the above neural network type operators and Voronovskaja type theorems are again proved. At the end of the paper, numerical results are provided.
doi_str_mv 10.1007/s00009-020-01513-7
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subjects Asymptotic series
Convergence
Goats
Mathematics
Mathematics and Statistics
Neural networks
Operators
Spline functions
Theorems
title Voronovskaja Type Theorems and High-Order Convergence Neural Network Operators with Sigmoidal Functions
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