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Applied and Computational Harmonic Analysis, ISSN 1063-5203, 11/2019, Volume 47, Issue 3, pp. 702 - 729
The paper discusses the construction of high dimensional spatial discretizations for arbitrary multivariate trigonometric polynomials, where the frequency... 
Sparse multivariate trigonometric polynomials | Lattice rule | Multiple rank-1 lattice | Fast Fourier transform | MATHEMATICS, APPLIED | PERIODIC-FUNCTIONS | APPROXIMATION | RANK-1 LATTICE
Journal Article
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, ISSN 0895-4798, 2011, Volume 32, Issue 4, pp. 1095 - 1124
Recent work on eigenvalues and eigenvectors for tensors of order m >= 3 has been motivated by applications in blind source separation, magnetic resonance... 
MATHEMATICS, APPLIED | APPROXIMATION | l-eigenpairs | LARGEST EIGENVALUE | RANK-1 | tensor eigenvalues | rank-1 approximation | shifted symmetric higher-order power method (SS-HOPM) | symmetric higher-order power method (S-HOPM) | E-eigenpairs | Z-eigenpairs | Mathematics - Numerical Analysis
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 04/2020, Volume 102, p. 106140
For the best sparse rank-1 approximation to higher-order tensors, we propose a proximal alternating minimization method in which each iteration can be easily... 
Sparse rank-1 approximation | Proximal alternating minimization | [formula omitted]-regularization
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2012, Volume 33, Issue 3, pp. 806 - 821
Journal Article
Electronic Journal of Linear Algebra, ISSN 1537-9582, 2019, Volume 35, Issue 1, pp. 24 - 34
Let H-n(F) be the space of all n x n upper Hessenberg matrices over a field F, where n is a positive integer greater than two. In this paper, surjective... 
Rank-1 preservers | Additive maps | Hessenberg matrices | MATHEMATICS
Journal Article
Signal Processing, ISSN 0165-1684, 05/2020, Volume 170, p. 107432
Separating singing voice from a musical mixture remains an important task in the field of music information retrieval. Recent studies on singing voice... 
Singing voice separation | Non-negative rank-1 constraint | Robust principal component analysis
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 06/2013, Volume 438, Issue 11, pp. 4166 - 4182
Many important spectral properties of nonnegative matrices have recently been successfully extended to higher order nonnegative tensors; for example, see... 
Nonnegative tensor | Perron–Frobenius | 15A69 | 15A18 | Perron-Frobenius | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | RANK-1 | PERRON-FROBENIUS THEOREM
Journal Article
SIAM Journal on Optimization, ISSN 1052-6234, 2016, Volume 26, Issue 1, pp. 171 - 196
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2011, Volume 32, Issue 4, pp. 1095 - 1124
Journal Article
New Journal of Physics, ISSN 1367-2630, 07/2010, Volume 12, Issue 7, p. 073025
The geometric measure of entanglement is investigated for permutation symmetric pure states of multipartite qubit systems, in particular the question of... 
PHASE | SPIN | PHYSICS, MULTIDISCIPLINARY | ORDER TENSORS | QUANTUM | RANK-1 APPROXIMATION | REPRESENTATION | Physics - Quantum Physics
Journal Article
Optimization Methods and Software, ISSN 1055-6788, 03/2020, Volume 35, Issue 2, pp. 416 - 438
Finding the symmetric rank-1 approximation to a given symmetric tensor is an important problem due to its wide applications and its close relationship to the... 
symmetric tensor | Rank-1 approximation | 65K05 | 90C22 | 90C26 | Bose-Einstein condensate | proximal alternating linearized minimization
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2018, Volume 39, Issue 3, pp. 1095 - 1115
This paper revisits the problem of finding the best rank-1 approximation to a symmetric tensor and makes three contributions. First, in contrast to the many... 
Best rank-1 approximation | Symmetric tensor | Convergence analysis | Singular value decomposition | symmetric tensor | best rank-1 approximation | MATHEMATICS, APPLIED | OPTIMIZATION | convergence analysis | singular value decomposition
Journal Article
Journal of Machine Learning Research, ISSN 1532-4435, 10/2017, Volume 18, pp. 1 - 28
Dictionaries are collections of vectors used for the representation of a class of vectors in Euclidean spaces. Recent research on optimal dictionaries is... 
Rank-1 decomposition | 2-optimal dictionary | Finite tight frames | l-optimal dictionary | CONTROLLABILITY | rank-1 decomposition | finite tight frames | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 10/2018, Volume 555, pp. 53 - 69
This paper revisits the classical problem of finding the best rank-1 approximation to a generic tensor. The main focus is on providing a mathematical proof for... 
Best rank-1 tensor approximation | Singular value decomposition | MATHEMATICS | MATRIX | MATHEMATICS, APPLIED | SYMMETRIC TENSORS | ALTERNATING LEAST-SQUARES | ORDER TENSORS
Journal Article
Communications in Algebra, ISSN 0092-7872, 11/2017, Volume 45, Issue 11, pp. 4696 - 4706
Let n≥3 be a natural number. Let M n ( ) be the ring of all n×n matrices over a noncommutative division ring . In the present paper, we will find the... 
division rings | functional identities | rank-1 matrices | 16R60 | Commuting maps | MATHEMATICS | Mathematical analysis | Matrix methods | Maps
Journal Article
Neurocomputing, ISSN 0925-2312, 07/2019, Volume 350, pp. 44 - 52
In this paper, a novel blind separation method for monaural singing voice based on an extension of robust principal component analysis (RPCA) using a rank-1... 
Robust principal component analysis | Rank-1 constraint | Monaural singing voice separation | Coalescent masking | Vocal activity detection | MELODY EXTRACTION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Journal Article
IEEE Transactions on Image Processing, ISSN 1057-7149, 10/2019, Volume 28, Issue 10, pp. 4730 - 4745
Journal Article
International Journal of Computer Vision, ISSN 0920-5691, 2019, Volume 127, Issue 8, pp. 1063 - 1083
High-order motion information is important in multi-target tracking (MTT) especially when dealing with large inter-target ambiguities. Such high-order... 
Multi-target tracking | Rank-1 tensor approximation | Multi-dimensional assignment | Data association | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ALGORITHM | Algorithms | Multiple target tracking | Pedestrians | Tensors | Approximation | Mathematical analysis | Tensor analysis | Iterative algorithms | Iterative methods
Journal Article
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