Recursive decomposition of multidimensional tensors

DOI10.1134/S1064562409040036zbMath1183.15024OpenAlexW2039001924MaRDI QIDQ845132

Evgenij E. Tyrtyshnikov, Ivan V. Oseledets

Publication date: 5 February 2010

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562409040036

zbMATH Keywords

multidimensional tensorsrecursive decomposition

Mathematics Subject Classification ID

Trees (05C05) Vector and tensor algebra, theory of invariants (15A72) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (11)

Computations in quantum tensor networks ⋮ Low-rank tensor methods for partial differential equations ⋮ Variational calculus with sums of elementary tensors of fixed rank ⋮ Adaptive near-optimal rank tensor approximation for high-dimensional operator equations ⋮ On manifolds of tensors of fixed TT-rank ⋮ Approximation rates for the hierarchical tensor format in periodic Sobolev spaces ⋮ Error Analysis of TT-Format Tensor Algorithms ⋮ Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations ⋮ On the interconnection between the higher-order singular values of real tensors ⋮ \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling ⋮ TT-cross approximation for multidimensional arrays

Cites Work

• Approximate iterations for structured matrices
• A theory of pseudoskeleton approximations
• Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
• Numerical operator calculus in higher dimensions
• Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time
• Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem

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