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Computing symmetric rank for symmetric tensors

Alessandra Bernardi 1 Alessandro Gimigliano 2 Monica Idà 2 
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (1965 - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We consider the problem of determining the symmetric tensor rank for symmetric tensors with an algebraic geometry approach. We give algorithms for computing the symmetric rank for $2\times \cdots \times 2$ tensors and for tensors of small border rank. From a geometric point of view, we describe the symmetric rank strata for some secant varieties of Veronese varieties.
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Submitted on : Monday, November 28, 2011 - 10:39:29 PM
Last modification on : Thursday, August 4, 2022 - 4:52:37 PM
Long-term archiving on: : Wednesday, February 29, 2012 - 2:31:17 AM


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Alessandra Bernardi, Alessandro Gimigliano, Monica Idà. Computing symmetric rank for symmetric tensors. Journal of Symbolic Computation, 2011, 46 (1), pp.34-53. ⟨10.1016/j.jsc.2010.08.001⟩. ⟨hal-00645973⟩



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