Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices
Joint Authors
Tang, Ying
Zou, Xiongfei
Bu, Shirong
Luo, Zhengxiang
Zhong, Shouming
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-03-20
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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, as well 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.
American Psychological Association (APA)
Zou, Xiongfei& Tang, Ying& Bu, Shirong& Luo, Zhengxiang& Zhong, Shouming. 2013. Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-483924
Modern Language Association (MLA)
Zou, Xiongfei…[et al.]. Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices. Journal of Applied Mathematics No. 2013 (2013), pp.1-13.
https://search.emarefa.net/detail/BIM-483924
American Medical Association (AMA)
Zou, Xiongfei& Tang, Ying& Bu, Shirong& Luo, Zhengxiang& Zhong, Shouming. Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-483924
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-483924