Estimating a Few Extreme Singular Values and Vectors for Large-Scale Matrices in Tensor Train Format

DOI10.1137/140983410zbMath1319.65029arXiv1410.6895OpenAlexW3105925603WikidataQ60486500 ScholiaQ60486500MaRDI QIDQ5265006

Namgil Lee, Andrzej Cichocki

Publication date: 21 July 2015

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.6895

zbMATH Keywords

algorithmcomputational complexitynumerical examplesingular value decompositionrandom matrixtridiagonal matrixHankel and Toeplitz matricescurse of dimensionalityHilbert matrixmatrix factorizationtensor networklow-rank tensor approximationmatrix product operatorsymmetric eigenvalue decompositionalternating least squares methodtensor train decomposition

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52) Complexity and performance of numerical algorithms (65Y20) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (7)

Randomized algorithms for the approximations of Tucker and the tensor train decompositions ⋮ Computing Low-Rank Approximations of Large-Scale Matrices with the Tensor Network Randomized SVD ⋮ Error Analysis of TT-Format Tensor Algorithms ⋮ Block tensor train decomposition for missing data estimation ⋮ Low-rank tensor train for tensor robust principal component analysis ⋮ Regularized Computation of Approximate Pseudoinverse of Large Matrices Using Low-Rank Tensor Train Decompositions ⋮ Fundamental tensor operations for large-scale data analysis using tensor network formats

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