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73,415
Symmetric tensors and symmetric tensor rank
- Scientific Computing and Computational Mathematics (SCCM
, 2006
"... Abstract. A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric sum of outer product of vectors. A rank-1 order-k tensor is the outer product of k non-zero vectors. An ..."
Abstract
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Cited by 101 (22 self)
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Abstract. A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric sum of outer product of vectors. A rank-1 order-k tensor is the outer product of k non-zero vectors
Giorgio Ottaviani Tutorial on Tensor rank and tensor decomposition
"... Tutorial: A brief survey on tensor rank and tensor decomposition, from a geometric perspective. Workshop ..."
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Tutorial: A brief survey on tensor rank and tensor decomposition, from a geometric perspective. Workshop
2 The tensor rank decomposition 3 The Schmidt–Eckart–Young decomposition Definition
, 2015
"... a generic tensor rank decomposition ..."
TENSOR RANK AND THE ILL-POSEDNESS OF THE BEST LOW-RANK APPROXIMATION PROBLEM
"... There has been continued interest in seeking a theorem describing optimal low-rank approximations to tensors of order 3 or higher, that parallels the Eckart–Young theorem for matrices. In this paper, we argue that the naive approach to this problem is doomed to failure because, unlike matrices, te ..."
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Cited by 193 (13 self)
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There has been continued interest in seeking a theorem describing optimal low-rank approximations to tensors of order 3 or higher, that parallels the Eckart–Young theorem for matrices. In this paper, we argue that the naive approach to this problem is doomed to failure because, unlike matrices
Tensor rank-one decomposition of probability tables
, 2005
"... We propose a new additive decomposition of probability tables- tensor rank-one decomposition. The basic idea is to decompose a probability table into a series of tables, such that the table that is the sum of the series is equal to the original table. Each table in the series has the same domain as ..."
Abstract
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Cited by 4 (0 self)
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We propose a new additive decomposition of probability tables- tensor rank-one decomposition. The basic idea is to decompose a probability table into a series of tables, such that the table that is the sum of the series is equal to the original table. Each table in the series has the same domain
Tensor rank, invariants, inequalities, and applications
- SIAM Journal on Matrix Analysis and Applications
, 2013
"... ar ..."
Boolean Circuits, Tensor Ranks, And Communication Complexity
- SIAM J. ON COMPUTING
, 1997
"... We investigate two methods for proving lower bounds on the size of small depth circuits, namely the approaches based on multiparty communication games and algebraic characterizations extending the concepts of the tensor rank and rigidity of matrices. Our methods are combinatorial, but we think that ..."
Abstract
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Cited by 29 (2 self)
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We investigate two methods for proving lower bounds on the size of small depth circuits, namely the approaches based on multiparty communication games and algebraic characterizations extending the concepts of the tensor rank and rigidity of matrices. Our methods are combinatorial, but we think
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