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Matrices with low-rank structure are ubiquitous in scientific computing.
Distribution of eigenvalues for some sets of random matrices
V. A. Mar c · 1967
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R. Mathias · 1990
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Local operator theory, random matrices and Banach spaces
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On the distribution of the largest eigenvalue in principal components analysis
I. M. Johnstone · 2001
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A well-conditioned estimator for large-dimensional covariance matrices
O. Ledoit and M. Wolf · 2004
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Spectrum estimation for large dimensional covariance matrices using random matrix theory
N. El Karoui · 2008
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Finite sample approximation results for principal component analysis: A matrix perturbation approach
B. Nadler · 2008
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N. R. Rao, J. A. Mingo, R. Speicher, and A. Edelman · 2008
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V. Rokhlin and M. Tygert · 2008
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G. Ballard, J. Demmel, and I. Dumitriu · 2010
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M. Rudelson and R. Vershynin · 2010
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Tail bounds for all eigenvalues of a sum of random matrices
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Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
N. Halko, P.-G. Martinsson, and J. A. Tropp · 2011
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Improved analysis of the subsampled randomized Hadamard transform
J. A. Tropp · 2011
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Matrix Computations
G. H. Golub and C. F. Van Loan · 2012
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Nonlinear shrinkage estimation of large-dimensional covariance matrices
O. Ledoit and M. Wolf · 2012
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Eigenvalues of a matrix in the streaming model
A. Andoni and H. L. Nguyễn · 2013
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Improved matrix algorithms via the subsampled randomized Hadamard transform
C. Boutsidis and A. Gittens · 2013
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Fast matrix rank algorithms and applications
H. Y. Cheung, T. C. Kwok, and L. C. Lau · 2013
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The effect of coherence on sampling from matrices with orthonormal columns, and preconditioned least squares problems
I. C. Ipsen and T. Wentworth · 2014
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Low-rank approximation and regression in input sparsity time
K. L. Clarkson and D. P. Woodruff · 2017
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Concentration inequalities and moment bounds for sample covariance operators
V. Koltchinskii and K. Lounici · 2017
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Fast estimation of approximate matrix ranks using spectral densities
S. Ubaru, Y. Saad, and A.-K. Seghouane · 2017
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High-dimensional probability: An introduction with applications in data science
R. Vershynin · 2018
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Efficient randomized algorithms for the fixed-precision low-rank matrix approximation
W. Yu, Y. Gu, and Y. Li · 2018
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Fast Direct Solvers for Elliptic PDEs
P.-G. Martinsson · 2019
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Sparser Johnson-Lindenstrauss transforms
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Streaming low-rank matrix approximation with an application to scientific simulation
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Why are big data matrices approximately low rank?
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Randomized projection for rank-revealing matrix factorizations and low-rank approximations
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Analytical nonlinear shrinkage of large-dimensional covariance matrices
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Randomized numerical linear algebra: Foundations and algorithms
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Fast and stable randomized low-rank matrix approximation
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Hashing embeddings of optimal dimension, with applications to linear least squares
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