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Randomized SVD has become an extremely successful approach for efficiently computing a low-rank approximation of matrices.
Über die praktische auflösung von integralgleichungen mit anwendungen auf randwertaufgaben
E. J. Nyström · 1930
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The distribution of eigenvalues in certain sets of random matrices
L. A. Pastur and V. A. Marchenko · 1967
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Rank revealing QR factorizations
T. F. Chan · 1987
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Topics in Matrix Analysis
R. A. Horn and C. R. Johnson · 1991
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Improved error bounds for underdetermined system solvers
J. W. Demmel and N. J. Higham · 1993
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Matrix Computations
G. H. Golub and C. F. Van Loan · 1996
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Matrix Computations
G. H. Golub and C. F. Van Loan · 1996
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Efficient algorithms for computing a strong rank-revealing QR factorization
M. Gu and S. C. Eisenstat · 1996
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A theory of pseudoskeleton approximations
S. A. Goreinov, E. E. Tyrtyshnikov, and N. L. Zamarashkin · 1997
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Numerical Linear Algebra
L. N. Trefethen and D. Bau · 1997
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Local operator theory, random matrices and banach spaces
K. R. Davidson and S. J. Szarek · 2001
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Using the Nyström method to speed up kernel machines
C. K. Williams and M. Seeger · 2001
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Accuracy and Stability of Numerical Algorithms
N. J. Higham · 2002
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Learning with kernels: support vector machines, regularization, optimization, and beyond
B. Schölkopf and A. J. Smola · 2002
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Low-rank approximations with sparse factors I: Basic algorithms and error analysis
Z. Zhang, H. Zha, and H. Simon · 2002
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Spectral grouping using the nystrom method
C. Fowlkes, S. Belongie, F. Chung, and J. Malik · 2004
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Condition numbers of gaussian random matrices
Z. Chen and J. J. Dongarra · 2005
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Improved approximation algorithms for large matrices via random projections
T. Sarlos · 2006
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The many proofs of an identity on the norm of oblique projections
D. B. Szyld · 2006
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Fast linear algebra is stable
J. Demmel, I. Dumitriu, and O. Holtz · 2007
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A fast randomized algorithm for overdetermined linear least-squares regression
V. Rokhlin and M. Tygert · 2008
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A fast randomized algorithm for the approximation of matrices
F. Woolfe, E. Liberty, V. Rokhlin, and M. Tygert · 2008
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Numerical linear algebra in the streaming model
K. L. Clarkson and D. P. Woodruff · 2009
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CUR matrix decompositions for improved data analysis
M. W. Mahoney and P. Drineas · 2009
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Smallest singular value of a random rectangular matrix
M. Rudelson and R. Vershynin · 2009
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Blendenpik: Supercharging lapack’s least-squares solver
H. Avron, P. Maymounkov, and S. Toledo · 2010
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Dimensionality reduction for k-means clustering and low rank approximation
M. B. Cohen, S. Elder, C. Musco, C. Musco, and M. Persu · 2015
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Subspace iteration randomization and singular value problems
M. Gu · 2015
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Roundoff error analysis of the CholeskyQR2 algorihm
Y. Yamamoto, Y. Nakatsukasa, Y. Yanagisawa, and T. Fukaya · 2015
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Optimal principal component analysis in distributed and streaming models
C. Boutsidis, D. P. Woodruff, and P. Zhong · 2016
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Revisiting the Nyström method for improved large-scale machine learning
A. Gittens and M. W. Mahoney · 2016
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Randomized methods for matrix computations
P.-G. Martinsson · 2016
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A universality result for the smallest eigenvalues of certain sample covariance matrices
O. N. Feldheim and S. Sodin · 2010
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The University of Florida sparse matrix collection
T. A. Davis and Y. Hu · 2011
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Faster least squares approximation
P. Drineas, M. W. Mahoney, S. Muthukrishnan, and T. Sarlós · 2011
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The spectral norm error of the naive Nyström extension
A. Gittens · 2011
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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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A DEIM induced CUR factorization
D. C. Sorensen and M. Embree · 2016
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J. Upadhyay · 2016
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A short proof of the Marchenko–Pastur theorem
P. Yaskov · 2016
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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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Algorithm 971: An implementation of a randomized algorithm for principal component analysis
H. Li, G. C. Linderman, A. Szlam, K. P. Stanton, Y. Kluger, and M. Tygert · 2017
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Sublinear time low-rank approximation of positive semidefinite matrices
C. Musco and D. P. Woodruff · 2017
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Fixed-rank approximation of a positive-semidefinite matrix from streaming data
J. A. Tropp, A. Yurtsever, M. Udell, and V. Cevher · 2017
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Practical sketching algorithms for low-rank matrix approximation
J. A. Tropp, A. Yurtsever, M. Udell, and V. Cevher · 2017
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Low rank approximation of a sparse matrix based on lu factorization with column and row tournament pivoting
L. Grigori, S. Cayrols, and J. W. Demmel · 2018
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On the existence of a nearly optimal skeleton approximation of a matrix in the Frobenius norm
N. L. Zamarashkin and A. I. Osinsky · 2018
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Low-rank approximation in the Frobenius norm by column and row subset selection
A. Cortinovis and D. Kressner · 2019
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J. Demmel, L. Grigori, and A. Rusciano · 2019
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Streaming low-rank matrix approximation with an application to scientific simulation
J. A. Tropp, A. Yurtsever, M. Udell, and V. Cevher · 2019
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Randomized numerical linear algebra: Foundations and algorithms
P.-G. Martinsson and J. A. Tropp · 2020
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