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| 1 | 基于B样条神经网络算子的散乱数据插值显示文摘目的:研究散乱数据神经网络算子的插值逼近性。方法:首先,将一维B样条函数变换成一类Sigmoid函数。然后,将若干个上述Sigmoid函数相乘得到的多元函数作为激活函数。结果:构造了一类多元神经网络插值算子,以函数的光滑模作为逼近度量,借助散乱数据网格范数,估计该类神经网络算子对有界域上的多元连续函数的逼近误差。特别地,给出一些具体的数值仿真算例进一步验证理论结果。结论:B样条神经网络算子对散乱数据有较好的插值逼近性。 | 徐慧芳 曹飞龙 | 2019 | 中国计量大学学报2019，30，4： | 2 |
| 2 | The construction and approximation of feedforward neural network with hyperbolic tangent function显示文摘In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tangent activation functionFirstly, an equation of partitions of unity for the hyperbolic tangent function is givenThen, two kinds of quasi-interpolation type neural network operators are constructed to approximate univariate and bivariate functions, respectivelyAlso, the errors of the approximation are estimated by means of the modulus of continuity of functionMoreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated. | CHEN Zhi-xiang CAO Fei-long | 2015 | Applied Mathematics(A Journal of Chinese Universities)2015，30，2： | 1 |
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