Approximation by superpositions of a sigmoidal function

DOI10.4171/ZAA/1156zbMath1062.41015OpenAlexW1978110782MaRDI QIDQ5917524

Giuseppe Marino, Grzegorz Lewicki

Publication date: 6 September 2004

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/zaa/1156

zbMATH Keywords

sigmoidal functionHölder continuity propertyphi-variation, uniform approximation

Mathematics Subject Classification ID

Rate of convergence, degree of approximation (41A25) Approximation by other special function classes (41A30)

Related Items (13)

Global Mittag-Leffler stability of complex valued fractional-order neural network with discrete and distributed delays ⋮ Max-product neural network and quasi-interpolation operators activated by sigmoidal functions ⋮ Solving numerically nonlinear systems of balance laws by multivariate sigmoidal functions approximation ⋮ Neural network interpolation operators activated by smooth ramp functions ⋮ Neural network operators: constructive interpolation of multivariate functions ⋮ Solving Volterra integral equations of the second kind by sigmoidal functions approximation ⋮ Approximation results for neural network operators activated by sigmoidal functions ⋮ Multivariate neural network operators with sigmoidal activation functions ⋮ A collocation method for solving nonlinear Volterra integro-differential equations of neutral type by sigmoidal functions ⋮ Interpolation by neural network operators activated by ramp functions ⋮ Convergence of a family of neural network operators of the Kantorovich type ⋮ Approximation by series of sigmoidal functions with applications to neural networks ⋮ Approximation of functions of finite variation by superpositions of a sigmoidal function.

Cites Work

• A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training
• Univariant approximation by superpositions of a sigmoidal function
• Multilayer feedforward networks are universal approximators
• Universal approximation bounds for superpositions of a sigmoidal function
• Approximation by superpositions of a sigmoidal function

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