Convergence Analysis on Neural Network for Eigenproblem

叶仲泉; 曾长修

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Convergence Analysis on Neural Network for Eigenproblem

更新时间：2025-12-08

- Convergence Analysis on Neural Network for Eigenproblem
- Acta Electronica Sinica Issue 1, (1997)
- 作者机构：
  
  1. 重庆大学系统工程及应用数学系
  2. 重庆大学自动化系
  3. 重庆大学系统工程及应用数学系重庆大学自动化系
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP183
- Published：1997
- 稿件说明：
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[1]叶仲泉,曾长修.特征神经网络收敛性分析[J].电子学报,1997(01):46-49.

叶仲泉, 曾长修. Convergence Analysis on Neural Network for Eigenproblem[J]. Acta Electronica Sinica, 1997, (1).
[1]叶仲泉,曾长修.特征神经网络收敛性分析[J].电子学报,1997(01):46-49. DOI：

叶仲泉, 曾长修. Convergence Analysis on Neural Network for Eigenproblem[J]. Acta Electronica Sinica, 1997, (1). DOI：

摘要

求矩阵的特征值与特征向量的问题是科学和技术中广泛遇到的问题．本文将实对称矩阵的特征问题转化为求非线性方程的解的问题，并建立了一连续时间动力学神经网络来探讨该非线性方程，在相当一般的条件下利用Ｌｙａｐｕｎｏｖ函数讨论了网络的稳定性与收敛性．

Abstract

Calculating eigenvalues and eigenvectors of a matrix is widely encountered in science and technology. In this paper we turn the eigenproblem of a real symmetric matrix into a nonlinear equation problem. Then we construct a neural network of continuous-time dynamical system to explore the above nonlinear equation. The stability and convergence of the network are investigated by using Lyapunov function under rather mild conditions.

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