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- Title
Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices.
- Authors
Xiongfei Zou; Ying Tang; Shirong Bu; Zhengxiang Luo; Shouming Zhong
- Abstract
This paper introduces a novel neural-network-based approach for extracting some eigenpairs of real normal matrices of order n. Based on the proposed algorithm, the eigenvalues that have the largest and smallest modulus, real parts, or absolute values of imaginary parts can be extracted, respectively, aswell as the corresponding eigenvectors. Although the ordinary differential equation on which our proposed algorithm is built is only n-dimensional, it can succeed to extract n-dimensional complex eigenvectors that are indeed 2n-dimensional real vectors. Moreover, we show that extracting eigen-pairs of general real matrices can be reduced to those of real normal matrices by employing the norm-reducing skill. Numerical experiments verified the computational capability of the proposed algorithm.
- Subjects
ARTIFICIAL neural networks; EIGENVECTORS; EIGENVALUES; MATRICES (Mathematics); DIFFERENTIAL equations; NUMERICAL analysis; COMPUTER algorithms
- Publication
Journal of Applied Mathematics, 2013, p1
- ISSN
1110-757X
- Publication type
Article
- DOI
10.1155/2013/597628