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Journal Article
Journal of computational physics, ISSN 0021-9991, 2019, Volume 377, Issue C, pp. 142 - 154
.... Representations such as the tensor tree perform near-optimally when the tree decomposition is chosen to reflect the correlation structure in question, but making such a choice is non-trivial and good... 
Tensor networks | Singular value decomposition | MATRIX | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | APPROXIMATION | FORMAT | NETWORKS | COMPUTATION | PHYSICS, MATHEMATICAL | Algorithms | Greedy algorithms | Computer memory | Tensors | Decomposition | Computational physics | Optimization | MATHEMATICS AND COMPUTING | Physics | Computer Science
Journal Article
Journal Article
SIAM journal on scientific computing, ISSN 1095-7197, 2011, Volume 33, Issue 5, pp. 2295 - 2317
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 09/2010, Volume 56, Issue 9, pp. 4402 - 4416
Journal Article
Applied and computational harmonic analysis, ISSN 1063-5203, 2018, Volume 44, Issue 2, pp. 246 - 272
.... Numerical examples, which illustrate the performance of the algorithm and compare it to other decomposition methods, are presented. 
Randomized algorithms | Matrix factorizations | Random matrices | LU decomposition | MONTE-CARLO ALGORITHMS | MATHEMATICS, APPLIED | APPROXIMATION | FACTORIZATIONS | HADAMARD-TRANSFORM | SPARSE | RANK | MODEL | MATRIX DECOMPOSITIONS | SMALLEST SINGULAR-VALUE | COMPUTATION | Computer science | Electrical engineering | Algorithms
Journal Article
SIAM journal on scientific computing, ISSN 1095-7197, 2018, Volume 40, Issue 5, pp. A3267 - A3292
Proper Orthogonal Decomposition (POD) is a widely used technique for the construction of low-dimensional approximation spaces from high-dimensional input data... 
Proper orthogonal decomposition | Model reduction | Distributed algorithms | Parallel algorithms | Singular value decomposition | parallel algorithms | MATHEMATICS, APPLIED | distributed algorithms | model reduction | proper orthogonal decomposition | ALGORITHMS | EQUATION | singular value decomposition
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2000, Volume 21, Issue 4, pp. 1253 - 1278
We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition... 
Higher-order tensor | Multilinear algebra | Singular value decomposition | MATHEMATICS, APPLIED | multilinear algebra | higher-order tensor | TUTORIAL | singular value decomposition | PARAFAC
Journal Article
Journal of Sound and Vibration, ISSN 0022-460X, 2002, Volume 252, Issue 3, pp. 527 - 544
In view of the increasing popularity of the application of proper orthogonal decomposition (POD... 
SYSTEM | ACOUSTICS | SINGULAR-VALUE DECOMPOSITION | MODES | MECHANICS | PHYSICAL INTERPRETATION | REDUCTION | DYNAMICS | VIBRATIONS | SIMULATION | FRICTIONALLY EXCITED BEAM | ENGINEERING, MECHANICAL
Journal Article
Journal of the American Statistical Association, ISSN 0162-1459, 01/2014, Volume 109, Issue 505, pp. 145 - 159
Journal Article
IEEE transactions on smart grid, ISSN 1949-3061, 2017, Volume 8, Issue 1, pp. 275 - 284
Journal Article
Proceedings of the National Academy of Sciences - PNAS, ISSN 1091-6490, 2009, Volume 106, Issue 3, pp. 697 - 702
Principal components analysis and, more generally, the Singular Value Decomposition are fundamental data analysis tools that express a data matrix in terms of a sequence of orthogonal or uncorrelated... 
Principal components analysis | Randomized algorithms | Interpretation | Statistical leverage | Singular value decomposition | MONTE-CARLO ALGORITHMS | REGRESSION | interpretation | randomized algorithms | MULTIDISCIPLINARY SCIENCES | PATTERNS | statistical leverage | singular value decomposition | principal components analysis | Electronic data processing | Usage | Algorithms | Approximation theory | Matrix decomposition | Methods | Physical Sciences
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 2005, Volume 396, Issue 1-3, pp. 373 - 384
Given a complex matrix H, we consider the decomposition H = QRP* where Q and P have orthonormal columns, and R is a real upper triangular matrix with diagonal elements equal to the geometric mean of the positive singular values of H... 
MIMO systems | Geometric mean decomposition | Unitary factorization | QR decomposition | Schur decomposition | Matrix factorization | Singular value decomposition | MATHEMATICS | matrix factorization | unitary factorization | MATHEMATICS, APPLIED | geometric mean decomposition | decomposition | schur decomposition | singular value
Journal Article