A Concise Functional Neural Network for Computing the Extremum Eigenpairs of Real Symmetric Matrices

  • Yiguang Liu
  • Zhisheng You
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3971)


Quick extraction of the extremum eigenpairs of a real symmetric matrix is very important in engineering. Using neural networks to complete this operation is in a parallel manner and can achieve high performance. So, this paper proposes a very concise functional neural network (FNN) to compute the largest (or smallest) eigenvalue and one corresponding eigenvector. After transforming the FNN into a differential equation, and obtaining the analytic solution, the convergence properties are completely analyzed. By this FNN, the method that can compute the extremum eigenpairs whether the matrix is non-definite, positive definite or negative definite is designed. Finally, three examples show the validity. Comparing with the other ones used in the same field, the proposed FNN is very simple and concise, so it is very easy to realize.


Large Eigenvalue Recurrent Neural Network Small Eigenvalue Real Symmetric Matrix Real Symmetric Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yiguang Liu
    • 1
  • Zhisheng You
    • 1
  1. 1.Institute of Image & Graphics, School of Computer Science and EngineeringSichuan UniversityChengduP.R. China

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