A concise functional neural network for computing the extremum eigenpairs of real symmetric matrices

Authors:
Yiguang Liu;Zhisheng You
Affiliations:
Institute of Image & Graphics, School of Computer Science and Engineering, Sichuan University, Chengdu, P.R. China;Institute of Image & Graphics, School of Computer Science and Engineering, Sichuan University, Chengdu, P.R. China
Venue:
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
Year:
2006

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Abstract

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.