[PDF] Top 20 Detecting the Rank of a Symmetric Tensor
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Detecting the Rank of a Symmetric Tensor
... with the problem of Canonical Polyadic (CP) decomposition of a given ...require the knowledge of the rank of the sought tensor ...determining ... Voir le document complet
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A Riemannian Newton Optimization Framework for the Symmetric Tensor Rank Approximation Problem
... THE SYMMETRIC TENSOR RANK APPROXIMATION PROBLEM ∗ RIMA KHOUJA † ‡ , HOUSSAM KHALIL † , AND BERNARD MOURRAIN ‡ ...Abstract. The symmetric tensor rank approximation ... Voir le document complet
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A continuous analogue of the tensor-train decomposition
... provide a computational methodology for approximating multivariate functions and computing with them in this ...on tensor-product grids and we do not a priori specify a tensor-product ... Voir le document complet
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Subtracting a best rank-1 approximation does not necessarily decrease tensor rank
... that a best rank-R approximation of an order-k tensor may not exist when R ≥ 2 and k ≥ ...poses a serious problem to data analysts using tensor ...best rank-1 ... Voir le document complet
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Subtracting a best rank-1 approximation may increase tensor rank
... provide a mathematical treatment of the (in)validity of a rank-1 deflation procedure for higher-order ...over the real field, with symmetric tensors as a ... Voir le document complet
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Skew-Symmetric Tensor Decomposition
... actually a presentation of (IX) as a skew-symmetric rank 3 ...tensor. The closure of the orbit of (X) fills the ambient space so (X) ... Voir le document complet
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Coupled tensor low-rank multilinear approximation for hyperspectral super-resolution
... use the number of groundtruth materials as the number of ...for the Indian Pines ...in the case F = 50 used in [8]. However, the case of STEREO F = 100 gives ... Voir le document complet
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New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields
... gives the result from Lemma 3.9 ii). On the other hand, we proceed as the preceding proof to prove that for k ≥ log 2 n 2 , Condition (2) is ...in the interval log 2 n 2 ; n − 3 since n − ... Voir le document complet
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Real and complex rank for real symmetric tensors with low complex symmetric rank
... Introduction 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 ... Voir le document complet
9
On the Growth of L2-Invariants of Locally Symmetric Spaces, II: Exotic Invariant Random Subgroups in Rank One
... on the geodesic α ⊂ T(Σ). Here, a pleated surface f : (Σ, d 0 ) −→ N is a map that is an isometric embedding on the complement of some geodesic lamination on (Σ, d 0 ...refer the ... Voir le document complet
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Non-iterative low-multilinear-rank tensor approximation with application to decomposition in rank-(1,L,L) terms
... (2) X ˆ = G n=1 N • U (n) , G • 1 U (1) • 2 . . . • N U (N ) , 39 ∗ The contents of this work have been partially submitted to the EUSIPCO’2017 conference [ 13 ]. † Univ. Grenoble Alpes, CNRS, ... Voir le document complet
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Low Rank Tensor Methods in Galerkin-based Isogeometric Analysis
... that the rank profile is related to the geometric complexity of the ...2D the rank (computed by SVD) is limited by the minimum number of basis functions in ... Voir le document complet
34
Stratification of the fourth secant variety of Veronese variety via the symmetric rank
... in the particular case of m = 1, is known since Sylvester ([12], [22], Theorem ...case the Veronese variety coincides with a rational normal ...for the general case with m ≥ 2. Both ... Voir le document complet
22
On minimal decompositions of low rank symmetric tensors
... is 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 ... Voir le document complet
27
Estimation of structured tensor models and recovery of low-rank tensors
... that a minimum has been reached, 1 we check whether the gradient of the cost function (see ...variant, the empirical cumulative distribution functions (c.d.f.) of the NSE ... Voir le document complet
239
Jacobi-type algorithm for low rank orthogonal approximation of symmetric tensors and its convergence analysis
... knowledge, the 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 ... Voir le document complet
20
Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
... in the Bayes optimal setting, a general expression for the mutual information has been proposed using heuristic statistical physics computations, and proven in few specific ...prove the ... Voir le document complet
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The Hankel transform of first- and second-order tensor fields: definition and use for modeling circularly symmetric leaky waveguides.
... modeling of elasti wave propagation in ir ularly symmetri media an be done using spa e integral transform in ylindri al oordinates and does not ne essitate a potential ...ontext, The Hankel transform ... Voir le document complet
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Decomposition of Low Rank Multi-Symmetric Tensor
... Partial Symmetric Tensor Decomposition Problem In this section we give the definition of a multi-symmetric tensor as a multi-homogeneous polynomial of ... Voir le document complet
13
Symmetric tensor rank with a tangent vector: a generic uniqueness theorem
... 3O, the case y = 3 of Lemma 1 applied to the blowing-up of P m at O 1 , ...that a general H ∈ |I W (d)| has an isolated singularity at O with multiplicity at most ...is a unique ... Voir le document complet
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