Sets Computing the Symmetric Tensor Rank

被引：12

作者：

Ballico, Edoardo ^{[1
]}

Chiantini, Luca ^{[2
]}

机构：

[1] Univ Trento, Dipartimento Matemat, I-38123 Povo, TN, Italy

[2] Univ Siena, Dipartimento Sci Matemat & Informat R Magari, I-53100 Siena, Italy

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2013年 / 10卷 / 02期

关键词：

Symmetric tensor rank; Veronese embedding;

D O I：

10.1007/s00009-012-0214-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let denote the degree d Veronese embedding of . For any , the symmetric tensor rank sr(P) is the minimal cardinality of a set spanning P. Let be the set of all such that computes sr(P). Here we classify all such that sr(P) < 3d/2 and sr(P) is computed by at least two subsets of . For such tensors , we prove that has no isolated points.

引用

页码：643 / 654

页数：12

共 50 条

[1] Sets Computing the Symmetric Tensor Rank
Edoardo Ballico
Luca Chiantini
Mediterranean Journal of Mathematics, 2013, 10 : 643 - 654
[2] A CONVERGENCE ANALYSIS FOR AN ALGORITHM COMPUTING A SYMMETRIC LOW RANK ORTHOGONAL APPROXIMATION OF A SYMMETRIC TENSOR
Du, Wenxin
Hu, Shenglong
PACIFIC JOURNAL OF OPTIMIZATION, 2022, 18 (01): : 119 - 138
[3] SYMMETRIC TENSORS AND SYMMETRIC TENSOR RANK
Comon, Pierre
Golub, Gene
Lim, Lek-Heng
Mourrain, Bernard
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2008, 30 (03) : 1254 - 1279
[4] Detecting the Rank of a Symmetric Tensor
Marmin, Arthur
Castella, Marc
Pesquet, Jean-Christophe
2019 27TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO), 2019,
[5] Computing symmetric rank for symmetric tensors
Bernardi, Alessandra
Gimigliano, Alessandro
Ida, Monica
JOURNAL OF SYMBOLIC COMPUTATION, 2011, 46 (01) : 34 - 53
[6] On the Non-Uniqueness of the Sets Computing a Partially Symmetric Rank at Most Three
Ballico, Edoardo
CONTEMPORARY MATHEMATICS, 2020, 1 (04): : 238 - 242
[7] Tensor ranks and symmetric tensor ranks are the same for points with low symmetric tensor rank
E. Ballico
Archiv der Mathematik, 2011, 96 : 531 - 534
[8] Tensor ranks and symmetric tensor ranks are the same for points with low symmetric tensor rank
Ballico, E.
ARCHIV DER MATHEMATIK, 2011, 96 (06) : 531 - 534
[9] Multiple points, scheme rank and symmetric tensor rank
Ballico, Edoardo
PORTUGALIAE MATHEMATICA, 2013, 70 (03) : 243 - 250
[10] LOW RANK SYMMETRIC TENSOR APPROXIMATIONS
Nie, Jiawang
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2017, 38 (04) : 1517 - 1540

← 1 2 3 4 5 →