Computing symmetric rank for symmetric tensors

Authors:
Alessandra Bernardi;Alessandro Gimigliano;Monica Idà
Affiliations:
CIRMFBK, Trento, Italy;Dip. di Matematica and C.I.R.A.M., Univ. degli Studi di Bologna, Italy;Dip. di Matematica, Univ. degli Studi di Bologna, Italy
Venue:
Journal of Symbolic Computation
Year:
2011

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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 2x...x2 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.