[PDF] Top 20 Real and complex rank for real symmetric tensors with low complex symmetric rank

... TENSORS WITH LOW COMPLEX SYMMETRIC RANK EDOARDO BALLICO, ALESSANDRA BERNARDI ...of real homogeneous polynomial P whose min- imal real and complex ... Voir le document complet

... algorithm for low rank orthogonal approximation of symmetric tensors and its convergence analysis 1 Jianze Li 2 , Konstantin Usevich 3 , and Pierre Comon 4 Abstract: In ... Voir le document complet

... Introduction Tensors have interested mathematicians and physicists since the nineteenth ...language for expressing certain natural ...of tensors. From the sixties onward, a growing interest in ... Voir le document complet

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

... i and z i ∈ S d i (hv 1 , v 2 i) such that P(d i + 1) = s − t, are uniquely determined by T ...2 and in Corollary 4, by introducing the notion of linearly general po- sition of a scheme (Definition 1), we ... Voir le document complet

... 36; and Me 4 WHT = 10, Me 8 WHT = 24 ...algorithm and the algorithms in [3-5] are shown in Tables 3 and ...the real additions compared to the algorithm in [3], but at the cost of a little more ... Voir le document complet

... matrices with entries in Q and Hankel structure, ...n and the problem of computing sample points in each connected compo- nent of the real algebraic set defined by the rank constraint ... Voir le document complet

... surrogate for the rank [9], Bayesian models [10], or on matrix unfoldings such as balanced matri- cization ...deal with the CP decomposition of a symmetric tensor, which has for ... Voir le document complet

... gap with the statistical physics conjectured formula (and rigorous upper bound from [Krzakala et ...conjecture and has interesting non-trivial implications on the computational complexity of these ... Voir le document complet

... WHT and one length- Modified WHT ...here and also provide a rigorous mathemat- ical proof of the algorithm as well as an in-depth analysis of its computational ...to complex signal channel ... Voir le document complet

... in Complex Elliptically Symmetric Distributions Stefano Fortunati, Member, IEEE, Alexandre Renaux, Member, IEEE, Fr´ed´eric Pascal, Senior Member, IEEE Abstract—Covariance matrices play a major role in ... Voir le document complet

... coincides with a rational normal curve. In [7] and [14] one can find an algebraic theoretical algorithm for the general case with m ≥ ...Problem and Question 1 have a very interesting ... Voir le document complet

... algorithms for decomposing a tensor array into a sum of rank-1 ...of symmetric tensors of any order but of dimension 2, which can be decomposed with the help of a Sylvester’s the- orem ... Voir le document complet

... (a symmetric tensor) of type (1). Unfortunately, for a given P ∈ P N , we only have the inequality sbr(P ) ≤ sr(P ...). For the forms F for which the decomposition (1) is not unique, it makes ... Voir le document complet

... arithmetic for low rank ...associated with small singular values can be stored in lower precisions while preserving high accuracy ...needed for each singular vector. We apply this ... Voir le document complet

... Fig 2, provides a qualitative result of the estimated EAP. In the figure each glyph represents an iso-surface of the corresponding EAP. We first estimated the 4th order diffusion tensors using the Riemannian ... Voir le document complet

... IRT, real-valued and complex-valued Geometrical Optics (CGO) with Etalon Integrals (EI), and Adaptive Mesh Refinement ...forward and reflected wavefields, is addressed by the use ... Voir le document complet

... method for the decomposition of multi-symmetric tensors, based on simple linear algebra ...to tensors of low enough ...points and weights from eigenvectors of multiplication ... Voir le document complet

... 2009) and (Sylvester, 1886)); σ 2 (X n,d ), σ 3 (X n,d ) (any n,d, see Section 4); σ r (X 2,4 ), for r ≤ ...symmetric rank. Some of these results were known or partially known, with ... 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