Tensor ranks for the inversion of tensor-product binomials

DOI10.1016/j.cam.2010.02.006zbMath1197.15017OpenAlexW2022384382MaRDI QIDQ989123

Evgenij E. Tyrtyshnikov

Publication date: 27 August 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2010.02.006

zbMATH Keywords

inverse matricesKronecker productToeplitz matricestensor rankslow-rank matricesmultilevel matrices

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Multilinear algebra, tensor calculus (15A69) Vector spaces, linear dependence, rank, lineability (15A03)

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Cites Work

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• Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators I. Separable approximation of multi-variate functions
• Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics
• Kronecker-product approximations for some function-related matrices.
• Tensor properties of multilevel Toeplitz and related matrices
• Optimal Kronecker Product Approximation of Block Toeplitz Matrices
• Orthogonal Tensor Decompositions
• Combining Kronecker Product Approximation with Discrete Wavelet Transforms to Solve Dense, Function-Related Linear Systems
• A Multilinear Singular Value Decomposition
• Tensor approximations of matrices generated by asymptotically smooth functions
• Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
• Hierarchical Kronecker tensor-product approximations