The average number of critical rank-one approximations to a tensor

DOI10.1080/03081087.2016.1164660zbMath1358.15015arXiv1408.3507OpenAlexW210812591MaRDI QIDQ2953399

Jan Draisma, Emil Horobeţ

Publication date: 4 January 2017

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.3507

zbMATH Keywords

optimizationeigenvectorMonte Carlo methodscritical pointsingular valuerandom tensorscritical rank-one approximationsrank-one tensors

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Monte Carlo methods (65C05) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52) Multilinear algebra, tensor calculus (15A69) Vector spaces, linear dependence, rank, lineability (15A03) Critical points of functions and mappings on manifolds (58K05)

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Cites Work

• Eigenvectors of tensors and algorithms for Waring decomposition
• A central limit theorem for the determinant of a Wigner matrix
• The number of singular vector tuples and uniqueness of best rank-one approximation of tensors
• Symmetric tensor decomposition
• The number of eigenvalues of a tensor
• Best Low Multilinear Rank Approximation of Higher-Order Tensors, Based on the Riemannian Trust-Region Scheme
• Tensor rank is NP-complete
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• Decompositions of a Higher-Order Tensor in Block Terms—Part I: Lemmas for Partitioned Matrices
• Decompositions of a Higher-Order Tensor in Block Terms—Part II: Definitions and Uniqueness
• Decompositions of a Higher-Order Tensor in Block Terms—Part III: Alternating Least Squares Algorithms
• Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
• Symmetric Tensors and Symmetric Tensor Rank
• Most Tensor Problems Are NP-Hard

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