Decomposing tensors with structured matrix factors reduces to rank-1 approximations

Pierre Comon 1 Mikael Sorensen 1 Elias P. Tsigaridas 1, 2
2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : Tensor decompositions permit to estimate in a deterministic way the parameters in a multi-linear model. Applications have been already pointed out in antenna array processing and digital communications, among others, and are extremely attractive provided some diversity at the receiver is available. As opposed to the widely used ALS algorithm, non-iterative algorithms are proposed in this paper to compute the required tensor decomposition into a sum of rank-1 terms, when some factor matrices enjoy some structure, such as block-Hankel, triangular, band, etc.
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Pierre Comon, Mikael Sorensen, Elias P. Tsigaridas. Decomposing tensors with structured matrix factors reduces to rank-1 approximations. International Conference on Acoustics, Speech and Signal Processing, Mar 2010, Dallas, United States. pp.SPTM-P4. ⟨hal-00490248⟩

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