On Best Low Rank Approximation of Positive Definite Tensors (Q6166055)

scientific article; zbMATH DE number 7707727

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English	On Best Low Rank Approximation of Positive Definite Tensors	scientific article; zbMATH DE number 7707727

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instance of

scholarly article

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title

On Best Low Rank Approximation of Positive Definite Tensors (English)

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SIAM Journal on Matrix Analysis and Applications

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publication date

6 July 2023

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zbMATH Keywords

tensors

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canonical polyadic decomposition

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best low rank approximation

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border rank

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positive definite

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multilinear algebra

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multidimensional arrays

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1137/22m1494178

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cites work

Approximating Symmetric Positive Semidefinite Tensors of Even Order

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Pencil-Based Algorithms for Tensor Rank Decomposition are not Stable

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General procedure for multivariable polynomial positivity test with control applications

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Analysis of individual differences in multidimensional scaling via an $n$-way generalization of ``Eckart-Young'' decomposition

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Computing Tensor Eigenvalues via Homotopy Methods

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Positive Semidefinite Generalized Diffusion Tensor Imaging via Quadratic Semidefinite Programming

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Symmetric Tensors and Symmetric Tensor Rank

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Blind Identification of Underdetermined Mixtures by Simultaneous Matrix Diagonalization

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A Multilinear Singular Value Decomposition

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Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem

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On the Uniqueness of the Canonical Polyadic Decomposition of Third-Order Tensors---Part I: Basic Results and Uniqueness of One Factor Matrix

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On the Uniqueness of the Canonical Polyadic Decomposition of Third-Order Tensors---Part II: Uniqueness of the Overall Decomposition

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Generic Uniqueness Conditions for the Canonical Polyadic Decomposition and INDSCAL

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Guarantees for Existence of a Best Canonical Polyadic Approximation of a Noisy Low-Rank Tensor

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Remarks on the Symmetric Rank of Symmetric Tensors

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Nuclear norm of higher-order tensors

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On best rank one approximation of tensors

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The number of singular vector tuples and uniqueness of best rank-one approximation of tensors

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Q4917542

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A procedure for the positive definiteness of forms of even order

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Most Tensor Problems Are NP-Hard

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Learning mixtures of spherical gaussians

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Positive definiteness of diffusion kurtosis imaging

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Algebraic connectivity of an even uniform hypergraph

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Positivity and nonnegativity conditions of a quartic equation and related problems

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Tensor Decompositions and Applications

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On the non-existence of optimal solutions and the occurrence of ``degeneracy'' in the CANDECOMP/PARAFAC model

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Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics

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The <i>Z</i> -eigenvalues of a symmetric tensor and its application to spectral hypergraph theory

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Blind Multilinear Identification

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Inverses of $2\times 2$ block matrices

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Blind separation of instantaneous mixtures of nonstationary sources

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Eigenvalues of a real supersymmetric tensor

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$H^{+}$-eigenvalues of Laplacian and signless Laplacian tensors

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Tensor eigenvalues and their applications

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Spectral norm and nuclear norm of a third order tensor

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An even order symmetric $B$ tensor is positive definite

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Higher Order Positive Semidefinite Diffusion Tensor Imaging

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Semialgebraic Geometry of Nonnegative Tensor Rank

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Complex best $r$-term approximations almost always exist in finite dimensions

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A Counterexample to Comon's Conjecture

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Tensor Decomposition for Signal Processing and Machine Learning

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Canonical Polyadic Decomposition with a Columnwise Orthonormal Factor Matrix

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Degeneracy in Candecomp/Parafac explained for $p\times p\times 2$ arrays of rank $p+1$ or higher

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Low-Rank Approximation of Generic $p \timesq \times2$ Arrays and Diverging Components in the Candecomp/Parafac Model

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Q3998482

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Explicit Candecomp/Parafac solutions for a contrived 2$\times 2\times 2$ array of rank three

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Statistical analysis of finite mixture distributions

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A new class of positive semi-definite tensors

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Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation

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Identifiers

zbMATH Open document ID

1518.15029

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6166055