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| HAL : hal-00347139, version 1 |
| arXiv : 0905.0454 |
| Fiche détaillée |  Récupérer au format |
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| Mathematics in Signal Processing V, J. G. McWhirter and I. K. Proudler (Ed.) (2002) 1-24 |
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| Tensor Decompositions, State of the Art and Applications |
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| Pierre Comon 1 |
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| (2002) |
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| In this paper, we present a partial survey of the tools borrowed from tensor algebra, which have been utilized recently in Statistics and Signal Processing. It is shown why the decompositions well known in linear algebra can hardly be extended to tensors. The concept of rank is itself difficult to define, and its calculation raises difficulties. Numerical algorithms have nevertheless been developed, and some are reported here, but their limitations are emphasized. These reports hopefully open research perspectives for enterprising readers. |
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| 1 : | Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SIGNAL |
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Université de Nice Sophia Antipolis (UNS) – CNRS : UMR7271 |
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| Domaine | : | Informatique/Traitement du signal et de l'image Statistiques/Applications Sciences de l'ingénieur/Traitement du signal et de l'image |
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| tensor – rank – decomposition – approximate joint diagonalization – symmetric tensor – diagonalization – quantics – multivariate polynomials – Contrast – Parafac – Candecomp – Sylvester – eigenvalue – Courant-Fisher |
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| hal-00347139, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00347139 | |
| oai:hal.archives-ouvertes.fr:hal-00347139 | |
| Contributeur : Pierre Comon | |
| Soumis le : Dimanche 14 Décembre 2008, 18:29:00 | |
| Dernière modification le : Vendredi 26 Mars 2010, 10:03:06 | |
