{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T07:21:31Z","timestamp":1726471291975},"reference-count":27,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>This paper introduces a novel neural-network-based approach for extracting some eigenpairs of real normal matrices of order<jats:italic>n<\/jats:italic>. 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<jats:italic>n<\/jats:italic>-dimensional, it can succeed to extract<jats:italic>n<\/jats:italic>-dimensional complex eigenvectors that are indeed 2<jats:italic>n<\/jats:italic>-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.<\/jats:p>","DOI":"10.1155\/2013\/597628","type":"journal-article","created":{"date-parts":[[2013,3,20]],"date-time":"2013-03-20T21:02:05Z","timestamp":1363813325000},"page":"1-13","source":"Crossref","is-referenced-by-count":2,"title":["Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices"],"prefix":"10.1155","volume":"2013","author":[{"given":"Xiongfei","family":"Zou","sequence":"first","affiliation":[{"name":"School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu 610054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, 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