[PDF] Top 20 Symmetric tensors and symmetric tensor rank

... , AND BERNARD MOURRAIN ‡ Abstract. A symmetric tensor is a higher order generalization of a symmetric ...of symmetric tensors in relation to a decomposition into a ... Voir le document complet

... The tensor decomposition problem into a minimal sum of rank-1 terms, is raising interest and attention from many applied areas as signal processing for telecommu- nications [13], independent ... Voir le document complet

... equivalent symmetric CCPD, and no other equivalent CCPDs ...R and N , their assessment can be done a priori and reused for several different hypercubic tensors of same order, ... Voir le document complet

... orthogonal tensor decomposition was first tackled in [7], but appeared more formally in [20], in which many examples were presented to illustrate the difficulties of this type of decom- ...exists, and the ... Voir le document complet

... THE SYMMETRIC TENSOR RANK APPROXIMATION PROBLEM ∗ RIMA KHOUJA † ‡ , HOUSSAM KHALIL † , AND BERNARD MOURRAIN ‡ ...The symmetric tensor rank approximation problem (STA) ... Voir le document complet

... catalecticant matrix M r,d−r defined in Definition 17 does not have maximal rank. Remark 22. Any divisor D ⊂ C d , with deg D ≤ d + 1, is such that dim < D >= deg D − 1. The following result has been proved ... Voir le document complet

... X and that for each Q ∈ τ (X) \ X there is a unique O ∈ X and a unique tangent vector ν to X at O such that Q ∈ hνi and that hνi \ {O} is the contact locus of the tangent space T Q τ (X) with τ (X) \ ... Voir le document complet

... rays) and matrices (2-way ...a tensor form directly, that is to say, the observation diversity is insufficient either in time or ...partially symmetric or Hermitian due to the special algebraic ... Voir le document complet

... the rank of T must be smaller than its ...decomposable tensors; this constraint is less restrictive, but quite difficult to impose and still too ... Voir le document complet

... conjecture and has interesting non-trivial implications on the computational complexity of these ...on rank-one symmetric matrix estimation, our proof technique is readily extendable to more generic ... Voir le document complet

... decomposable tensors (Definition 2.1). The problem of tensor decomposition has been studied studied for many years and by researchers in many scientific areas as Algebraic Geometry (see for example ... Voir le document complet

... m,d and n := n m,d ...forms, and as the variety that parameterizes projective classes of symmetric tensors T ∈ V ⊗d where V is a vector space of dimension m + 1 and T = v ⊗d for certain ... Voir le document complet

... nonnegative and symmetric in two ...search and trust ...calculus and product operator ...rithms, and has been evaluated for each algorithm, allowing to fairly compare their ...array ... Voir le document complet

... Partial Symmetric Tensor Decomposition Problem In this section we give the definition of a multi-symmetric tensor as a multi-homogeneous polynomial of a different positive degree at each ... Voir le document complet

... the rank of f ? Can we provide a minimal Waring decomposition? For general forms of fixed degree and fixed number of variables, the value of the rank is known due to the result of ...classical ... Voir le document complet

... the rank of the sought tensor decomposition. Yet, determining the rank of a given tensor is generally ...the rank of a symmetric ...problem and we derive a sufficient ... Voir le document complet

... In the following section, we recall the method deduced from Sylvester’s theorem to decompose a binary form. In section 2, we give three equivalent formulations of the same problem, used and studied in different ... Voir le document complet

... iterative and lack a guarantee of global convergence [19] ...the rank to be much smaller than generic ...cumulant tensor, we refer the reader to ... Voir le document complet

... tions, and write their general element in each ...skew-symmetric rank 3 for v; in fact vi + vj would have skew-symmetric rank ...7 and l ∈ C 8 is general ... Voir le document complet

... Kashiwara and Vergne was a break- through in the …eld of analysis on Lie ...group and its Lie algebra, the use of speci…c subgroups ...groups and conjec- tured two general identities allowing an ... Voir le document complet