| 神经网络对Rd上连续函数最佳逼近的一个注记 |
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| 引用本文： | 谢林森,陆文秀,章莉.神经网络对Rd上连续函数最佳逼近的一个注记[J].南京大学学报(自然科学版),2013(1):34-39. |
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| 作者姓名： | 谢林森 陆文秀 章莉 |
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| 作者单位： | 丽水学院数学系;浙江师范大学数学系 |
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| 基金项目： | Supported by National Natural Science Foundation of China(11171137);Natural Science Foundation of Zhejiang Province(Y6110676) |
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| 摘 要： | 本文构造了一类单隐层神经网络，使其逼近Rd上连续函数的速度达到最佳代数多项式逼近速度，并刻划了该类单隐层神经网络的逼近性质．
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| 关 键 词： | 神经网络 逼近速度 最佳逼近多项式 |
A NOTE ON NEURAL NETWORKS FOR OPTIMAL APPROXIMATION OF CONTINUOUS FUNCTIONS IN Rd |
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| Xie Linsen Lishui University,Lishui PRC Lu Wenxiu and Zhang Li.A NOTE ON NEURAL NETWORKS FOR OPTIMAL APPROXIMATION OF CONTINUOUS FUNCTIONS IN Rd[J].Journal of Nanjing University: Nat Sci Ed,2013(1):34-39. |
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| Authors: | Xie Linsen Lishui University Lishui PRC Lu Wenxiu and Zhang Li |
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| Institution: | Xie Linsen (Lishui University,323000,Lishui PRC) Lu Wenxiu and Zhang Li (Zhejiang Normal University,321004,Jinhua PRC) |
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| Abstract: | In this paper, we construct a class of neural networks with single hidden layer, by which the approximation rate to continuous functions of d variables on any compact subset of Rd is the same as the case by the best algebraic polynomial. Fur- thermore, we characterize the approximation properties of this class of neural networks with single hidden laver. |
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| Keywords: | neural networks approximation rate the best algebraic polynomial ap-proximation |
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