Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices
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...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/597628 |
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| _version_ | 1832565640470200320 |
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| author | Xiongfei Zou Ying Tang Shirong Bu Zhengxiang Luo Shouming Zhong |
| author_facet | Xiongfei Zou Ying Tang Shirong Bu Zhengxiang Luo Shouming Zhong |
| author_sort | Xiongfei Zou |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3f7c00521575425795d281fa5b389996 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-3f7c00521575425795d281fa5b3899962025-02-03T01:07:04ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/597628597628Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real MatricesXiongfei Zou0Ying Tang1Shirong Bu2Zhengxiang Luo3Shouming Zhong4School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu 610054, ChinaSchool of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, ChinaSchool of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu 610054, ChinaSchool of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu 610054, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, ChinaThis 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.http://dx.doi.org/10.1155/2013/597628 |
| spellingShingle | Xiongfei Zou Ying Tang Shirong Bu Zhengxiang Luo Shouming Zhong Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices Journal of Applied Mathematics |
| title | Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices |
| title_full | Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices |
| title_fullStr | Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices |
| title_full_unstemmed | Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices |
| title_short | Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices |
| title_sort | neural network based approach for extracting eigenvectors and eigenvalues of real normal matrices and some extension to real matrices |
| url | http://dx.doi.org/10.1155/2013/597628 |
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