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A CUR approximation of a matrix $A$ is a particular type of low-rank approximation $A \approx C U R$, where $C$ and $R$ consist of columns and rows of $A$, respectively.
Rank revealing Q R QR factorizations
T. F. Chan · 1987
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On rank-revealing factorisations
S. Chandrasekaran and I. C. F. Ipsen · 1994
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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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Modifying two-sided orthogonal decompositions: Algorithms, implementation, and applications
P. A.-C. Yoon · 1996
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Algebraic complexity theory
P. Bürgisser, M. Clausen, and M. A. Shokrollahi · 1997
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LAPACK Users’ Guide
E. Anderson, Z. Bai, C. H. Bischof, S. Blackford, J. W. Demmel, J. J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. C. Sorensen · 1999
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Four algorithms for the efficient computation of truncated pivoted QR approximations to a sparse matrix
G. W. Stewart · 1999
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Approximation of boundary element matrices
M. Bebendorf · 2000
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A multilinear singular value decomposition
L. De Lathauwer, B. De Moor, and J. Vandewalle · 2000
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The maximal-volume concept in approximation by low-rank matrices
S. A. Goreinov and E. E. Tyrtyshnikov · 2001
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An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations
M. Barrault, Y. Maday, N. C. Nguyen, and A. T. Patera · 2004
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Fast Monte-Carlo algorithms for finding low-rank approximations
A. Frieze, R. Kannan, and S. Vempala · 2004
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Matrix approximation and projective clustering via volume sampling
A. Deshpande, L. Rademacher, S. Vempala, and G. Wang · 2006
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A randomized algorithm for a tensor-based generalization of the singular value decomposition
P. Drineas and M. W. Mahoney · 2007
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Relative-error C U R CUR matrix decompositions
P. Drineas, M. W. Mahoney, and S. Muthukrishnan · 2008
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Cross approximation of a multi-index array
S. A. Goreĭnov · 2008
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Matrix Mathematics
D. S. Bernstein · 2009
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An improved approximation algorithm for the column subset selection problem
C. Boutsidis, M. W. Mahoney, and P. Drineas · 2009
Cited alongside, same era.
On selecting a maximum volume sub-matrix of a matrix and related problems
A. Çivril and M. Magdon-Ismail · 2009
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Matrix computations
G. H. Golub and C. F. Van Loan · 2013
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Matrix analysis
R. A. Horn and C. R. Johnson · 2013
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An extension of Chebfun to two dimensions
A. Townsend and L. N. Trefethen · 2013
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Cauchy-Binet for pseudo-determinants
O. Knill · 2014
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Sketching as a tool for numerical linear algebra
D. P. Woodruff · 2014
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A new selection operator for the discrete empirical interpolation method—improved a priori error bound and extensions
Z. Drmač and S. Gugercin · 2016
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Tensor decompositions and applications
T. G. Kolda and B. W. Bader · 2009
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Nonlinear model reduction via discrete empirical interpolation
S. Chaturantabut and D. C. Sorensen · 2010
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Efficient volume sampling for row/column subset selection
A. Deshpande and L. Rademacher · 2010
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La budde’s method for computing characteristic polynomials
R. Rehman and I. C. Ipsen · 2011
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Computing characteristic polynomials from eigenvalues
R. Rehman and I. C. F. Ipsen · 2011
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On the low-rank approximation by the pivoted Cholesky decomposition
H. Harbrecht, M. Peters, and R. Schneider · 2012
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A. K. Saibaba · 2016
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A DEIM induced CUR factorization
D. C. Sorensen and M. Embree · 2016
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A DEIM induced CUR factorization
D. C. Sorensen and M. Embree · 2016
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Core-chasing algorithms for the eigenvalue problem
J. L. Aurentz, T. Mach, L. Robol, R. Vandebril, and D. S. Watkins · 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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A. Cortinovis, D. Kressner, and S. Massei · 2019
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