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- Publisher Website: 10.1080/03081087.2015.1071311
- Scopus: eid_2-s2.0-84938674578
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Article: An eigenvalue problem for even order tensors with its applications
Title | An eigenvalue problem for even order tensors with its applications |
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Authors | |
Keywords | eigenvalues circulant tensors eigenvectors higher order singular value decomposition multilevel matrices tensors Toeplitz tensors |
Issue Date | 2016 |
Citation | Linear and Multilinear Algebra, 2016, v. 64, n. 4, p. 602-621 How to Cite? |
Abstract | © 2015 Informa UK Limited, trading as Taylor & Francis Group. In this paper, we study an eigenvalue problem for even order tensors. Using the matrix unfolding of even order tensors, we can establish the relationship between a tensor eigenvalue problem and a multilevel matrix eigenvalue problem. By considering a higher order singular value decomposition of a tensor, we show that higher order singular values are the square root of the eigenvalues of the product of the tensor and its conjugate transpose. This result is similar to that in matrix case. Also we study an eigenvalue problem for Toeplitz/circulant tensors, and give the lower and upper bounds of eigenvalues of Toeplitz tensors. An application in image restoration is also discussed. |
Persistent Identifier | http://hdl.handle.net/10722/276692 |
ISSN | 2023 Impact Factor: 0.9 2023 SCImago Journal Rankings: 0.654 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Cui, Lu Bin | - |
dc.contributor.author | Chen, Chuan | - |
dc.contributor.author | Li, Wen | - |
dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:34:22Z | - |
dc.date.available | 2019-09-18T08:34:22Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | Linear and Multilinear Algebra, 2016, v. 64, n. 4, p. 602-621 | - |
dc.identifier.issn | 0308-1087 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276692 | - |
dc.description.abstract | © 2015 Informa UK Limited, trading as Taylor & Francis Group. In this paper, we study an eigenvalue problem for even order tensors. Using the matrix unfolding of even order tensors, we can establish the relationship between a tensor eigenvalue problem and a multilevel matrix eigenvalue problem. By considering a higher order singular value decomposition of a tensor, we show that higher order singular values are the square root of the eigenvalues of the product of the tensor and its conjugate transpose. This result is similar to that in matrix case. Also we study an eigenvalue problem for Toeplitz/circulant tensors, and give the lower and upper bounds of eigenvalues of Toeplitz tensors. An application in image restoration is also discussed. | - |
dc.language | eng | - |
dc.relation.ispartof | Linear and Multilinear Algebra | - |
dc.subject | eigenvalues | - |
dc.subject | circulant tensors | - |
dc.subject | eigenvectors | - |
dc.subject | higher order singular value decomposition | - |
dc.subject | multilevel matrices | - |
dc.subject | tensors | - |
dc.subject | Toeplitz tensors | - |
dc.title | An eigenvalue problem for even order tensors with its applications | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1080/03081087.2015.1071311 | - |
dc.identifier.scopus | eid_2-s2.0-84938674578 | - |
dc.identifier.volume | 64 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | 602 | - |
dc.identifier.epage | 621 | - |
dc.identifier.eissn | 1563-5139 | - |
dc.identifier.isi | WOS:000373702300004 | - |
dc.identifier.issnl | 0308-1087 | - |