A novel neural network approach for computing eigen-pairs of real antisymmetric matrices

Authors:
Hang Tan;Xianhe Huang;Huachun Tan;Ying Tang
Affiliations:
School of Automation and Engineering, University of Electronic Science and Technology of China, Chengdu, China;School of Automation and Engineering, University of Electronic Science and Technology of China, Chengdu, China;School of Mechanical and Vehicular Engineering, Beijing Institute of Technology, Beijing, China;School of Automation and Engineering, University of Electronic Science and Technology of China, Chengdu, China
Venue:
AICI'12 Proceedings of the 4th international conference on Artificial Intelligence and Computational Intelligence
Year:
2012

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Abstract

In the present paper, we focus on the problem how to compute all eigen-pairs of any real antisymmetric matrix by the conventional neural network approach without modification the original structure of the neural network. Given any n-dimensional real antisymmetric matrix, our proposed method is based on a n-dimensional ODEs and the preprocessing become comparatively easy. The contributions of this paper are mainly come from two aspects, on the one hand, we constructed the eigen-pairs relationship between those of symmetric matrix and anti-symmetric matrix; on the other hand, we presented a simple method to compute all eigen-pairs of any antisymmetric matrix. Simulations verify the computational capability of the proposed method.