| 神经网络算法在非线性系统中的应用研究 |
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| 引用本文： | 曾喆昭,王耀南.神经网络算法在非线性系统中的应用研究[J].湖南师范大学自然科学学报,2007,30(2):56-60. |
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| 作者姓名： | 曾喆昭 王耀南 |
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| 作者单位： | 1. 长沙理工大学电气与信息工程学院,中国,长沙,410076;湖南大学电气与信息工程学院,中国,长沙,410082
2. 长沙理工大学电气与信息工程学院,中国,长沙,410076 |
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| 基金项目： | 国家自然科学基金资助项目(60375001) |
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| 摘 要： | 研究了一种非线性系统分析的神经网络算法,提出并证明了该算法的收敛性定理,为学习率的取值范围提供了理论依据.解决了BP算法存在局部极小的问题,并给出了该算法的应用实例.研究结果表明,对于随机给定的初始点,该算法都能稳定收敛到它的一个实根,计算精度可控,而且能得到高精度解,因此,该算法是有效的.此外算法还可以用来解多元非线性方程和线性方程组.
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| 关 键 词： | 非线性系统 神经网络算法 收敛性 |
| 文章编号： | 1000-2537（2007）02-0056-05 |
The Application Research of Neural Network Algorithm in the Analysis of Nonlinear Systems |
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| ZENG Zhe-zhao,WANG Yao-nan.The Application Research of Neural Network Algorithm in the Analysis of Nonlinear Systems[J].Journal of Natural Science of Hunan Normal University,2007,30(2):56-60. |
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| Authors: | ZENG Zhe-zhao WANG Yao-nan |
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| Institution: | 1. College of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha 410076, China; 2. College of Electrical and Information Engineering, Hunan University, Changsha 410082, China |
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| Abstract: | The neural-network arithmetic to solve nonlinear systems was traversed.The convergence theorem of the arithmetic was presented and proved.This theorem gives theory gist to learning rate range.The local teeny problem of the BP arithmetic is overcome.The application examples are provided.The results show that the neural network can converge to a real solution stably for an arbitrarily given initial point of nonlinear systems of equations.The precision can be controlled and the high precision solution can be obtained.Therefore,this neural network arithmetic is effective.Furthermore,the arithmetic can also solve nonlinear equations in many variables and linear systems of equations. |
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| Keywords: | nonlinear systems neural network arithmetic convergence |
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