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In [13], Hillar and Lim famously demonstrated that "multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard".
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Some mathematical notes on three-mode factor analysis
L. R. Tucker · 1966
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Foundations of the parafac procedure: Models and conditions for an ”explanatory” multi-modal factor analysis
R. A. Harshman · 1969
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Analysis of individual differences in multidimensional scaling via an n-way generalization of ”eckart-young” decomposition
J. D. Carroll and J. J. Chang · 1970
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Candelinc: A general approach to multidimensional analysis of many-way arrays with linear constraints on parameters
J. D. Carroll, S. Pruzansky, and J. B. Kruskal · 1980
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Improving the speed of multi-way algorithms: Part ii
R. Bro and C. A. Andersson · 1998
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Singular values and eigenvalues of tensors: A variational approach
L.-H. Lim · 2005
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Eigenvalues of a real supersymmetric tensor
L. Qi · 2005
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Algorithm 862: Matlab tensor classes for fast algorithm prototyping
B. W. Bader and T. G. Kolda · 2006
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Structured rank- ( r 1 , ⋯ , r d ) (r_{1},\cdots,r_{d}) decomposition of function-related tensors in ℝ d \mathbb{R}^{d}
B. N. Khoromskij · 2006
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Multilinear operators for higher-order decompositions
T. G. Kolda and T. Gibson · 2006
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A comparison of algorithms for fitting the parafac model
G. Tomasi and R. Bro · 2006
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The Role of Tensor Rank in the Complexity Analysis of Bilinear Forms
D. Bini · 2007
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Low rank Tucker-type tensor approximation to classical potentials
B. N. Khoromskij and V. Khoromskaia · 2007
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On computing the underlying fiber directions from the diffusion orienta- tion distribution function
L. Bloy and R. Verma · 2008
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Symmetric tensors and symmetric tensor rank
P. Comon, G. Golub, L.H. Lim, and B. Mourrain · 2008
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A polynomial based approach to extract the maxima of an antipodally symmetric spherical function and its application to extract fiber directions from the orientation distribution function in diffusion mri
A. Ghosh, E. Tsigaridas, M. Descoteaux, P. Comon, B. Mourrain, and R. Deriche · 2008
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Most tensor problems are NP-hard
C.J. Hillar and L.-H. Lim · 2013
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Beyond convex relaxation: A polynomial-time non-convex optimization approach to network localization
S. Ji, K.-F. Sze, Z. Zhou, A. M.-C. So, and Y. Ye · 2013
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On the z-eigenvalues of the signless laplacian tensor for an even uniform hypergraph
J. Xie and A. Chang · 2013
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All real eigenvalues of symmetric tensors
C. Cui, Y. Dai, and J. Nie · 2014
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Computational complexity of tensor nuclear norm
S. Friedland and L.-H. Lim · 2014
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Semidefinite relaxations for best rank-1 tensor approximations
J. Nie and L. Wang · 2014
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T. G. Kolda and B. W. Bader · 2009
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Conditions for strong ellipticity and m-eigenvalues
L. Qi, H.-H. Dai, and D. Han · 2009
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Z-eigenvalue methods for a global polynomial optimization problem
L. Qi, F. Wang, and Y. Wang · 2009
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The geometric measure of multipartite entanglement and the singular values of a hypermatrix
J. J. Hilling and A. Sudbery · 2010
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Numerical Solution of the Hartree-Fock Equation by Multilevel Tensor-structured Methods
V. Khoromskaia · 2010
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Higher order positive semi-definite diffusion tensor imaging
L. Qi, G. Yu, and E. X. Wu · 2010
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Tensors: Geometry and applications
J. M. Landsberg · 2012
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Compact representation of multidimensional data using tensor rank-one decomposition
H. Wang and N. Ahuja · 2014
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Relations of the nuclear norms of a tensor and its matrix flattenings
S. Hu · 2015
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On cones of nonnegative quartic forms
B. Jiang, Z. Li, and S. Zhang · 2015
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Tensor principal component analysis via convex optimization
B. Jiang, S. Ma, and S. Zhang · 2015
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Tensor numerical methods for high-dimensional PDEs: Basic theory and initial applications. ESAIM: Proceedings and Surveys, 48:1–28, 2015
B. N. Khoromskij · 2015
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Generating polynomials and symmetric tensor decompositions
J. Nie · 2015
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