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| Oja神经网络模型的有限逸时性 | |
| 引用本文： | 刘力军,葛仁东,魏晓丹,邱天爽,崔强.Oja神经网络模型的有限逸时性[J].数学的实践与认识,2009,39(23). |
| 作者姓名： | 刘力军 葛仁东 魏晓丹 邱天爽 崔强 |
| 作者单位： | 1. 大连理工大学电子与信息工程学院,辽宁,大连,116024;大连民族学院理学院,辽宁,大连,116600 2. 大连民族学院理学院,辽宁,大连,116600 3. 大连民族学院计算机科学与工程学院,辽宁,大连,116600 4. 大连理工大学电子与信息工程学院,辽宁,大连,116024 5. 大连理工大学应用数学系,辽宁,大连,116024 |
| 基金项目： | 辽宁省教育厅科研项目，国家自然科学基金项目 |
| 摘 要： | O ja连续型全反馈神经网络模型可以有效计算实对称矩阵的主特征向量,该网络的动态行为由描述其模型的微分方程所决定,详细研究了O ja动力系统的稳定性问题.对于非正定实对称矩阵最大特征根为零,且至少有一特征根为负的情形,证明了从单位球外出发的解并不一定必然导致有限逸时,完善了O ja模型计算实对称矩阵主特征向量的收敛性结果,数值实验结果进一步验证了理论分析的正确性. |
| 关 键 词： | 实对称矩阵 主特征向量 神经网络 有限逸时 |
Limit-time Overflow of Oja Neural Network Model |
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| LIU Li-jun,GE Ren-dong,WEI Xiao-dan,QIU Tian-shuang,CUI Qiang.Limit-time Overflow of Oja Neural Network Model[J].Mathematics in Practice and Theory,2009,39(23). | |
| Authors: | LIU Li-jun GE Ren-dong WEI Xiao-dan QIU Tian-shuang CUI Qiang |
| Abstract: | Continuous full feedback neural network model can effectivley compute dominant eigenvector of a real symmetric matrix. Dynamical behavior of this network is determined by its corresponding differential equation. Stability of Oja dynamical system is thoroughly studied in this paper. For a non-positive real symmetric matrix, which has a largest zero eigenvalue and at least one negative eigenvalue, we proved that solution starting from outside of unit sphere does not necessarily lead to limit-time overflow, which truly improved the existing convergence results of Oja model for computing dominant eigenvector of real symmetric matrix. Theoretical results are further verified by numerical experiment. |
| Keywords: | symmetric matrix dominant eigenvector neural network limit-time overflow |
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