Convergence analysis of an SVD-based algorithm for the best rank-1 tensor approximation

DOI10.1016/j.laa.2018.06.006zbMath1397.65055OpenAlexW2806658157WikidataQ129729811 ScholiaQ129729811MaRDI QIDQ1654384

Delin Chu, Moody T. Chu, Yu Guan

Publication date: 8 August 2018

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

Full work available at URL: https://doi.org/10.1016/j.laa.2018.06.006

zbMATH Keywords

singular value decompositionbest rank-1 tensor approximation

Mathematics Subject Classification ID

Factorization of matrices (15A23) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Multilinear algebra, tensor calculus (15A69)

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Uses Software

• Algorithm 862
• GQTPAR

Cites Work

• Tensor Decompositions and Applications
• Symmetric tensor decomposition
• Numerical computation of an analytic singular value decomposition of a matrix valued function
• Differential equations for the analytic singular value decomposition of a matrix
• On the Łojasiewicz--Simon gradient inequality.
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• Numerical optimization for symmetric tensor decomposition
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• Jacobi Algorithm for the Best Low Multilinear Rank Approximation of Symmetric Tensors
• Local Convergence of the Alternating Least Squares Algorithm for Canonical Tensor Approximation
• On the Global Convergence of the Alternating Least Squares Method for Rank-One Approximation to Generic Tensors
• On best rank one approximation of tensors
• SVD-Based Algorithms for the Best Rank-1 Approximation of a Symmetric Tensor
• Computing a Trust Region Step
• Algorithm 862
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
• Symmetric Tensors and Symmetric Tensor Rank
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