Approximation by neural networks with sigmoidal functions.

*(English)*Zbl 1311.41015Summary: In this paper, we introduce a type of approximation operators of neural networks with sigmodal functions on compact intervals, and obtain the pointwise and uniform estimates of the approximation. To improve the approximation rate, we further introduce a type of combinations of neural networks. Moreover, we show that the derivatives of functions can also be simultaneously approximated by the derivatives of the combinations. We also apply our method to construct approximation operators of neural networks with sigmodal functions on infinite intervals.

##### MSC:

41A25 | Rate of convergence, degree of approximation |

41A46 | Approximation by arbitrary nonlinear expressions; widths and entropy |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

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\textit{D. S. Yu}, Acta Math. Sin., Engl. Ser. 29, No. 10, 2013--2026 (2013; Zbl 1311.41015)

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