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The CUR decomposition is a technique for low-rank approximation that selects small subsets of the columns and rows of a given matrix to use as bases for its column and rowspaces.
The approximation of one matrix by another of lower rank
Eckart, C., and Young, G · 1936
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Unitary triangularization of a nonsymmetric matrix
Householder, A. S · 1958
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Numerical linear algebra
Kahan, W · 1966
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On the stability of gauss-jordan elimination with pivoting
Peters, G., and Wilkinson, J. H · 1975
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Rank revealing qr factorizations
Chan, T. F · 1987
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$lu$ factorization algorithms on distributed-memory multiprocessor architectures
Geist, G. A., and Romine, C. H · 1988
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Average-case stability of gaussian elimination
Trefethen, L. N., and Schreiber, R. S · 1990
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Rank-revealing qr factorizations and the singular value decomposition
Hong, Y. P., and Pan, C.-T · 1992
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Matrix Computations
Golub, G. H., and Van Loan, C. F · 1996
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Efficient algorithms for computing a strong rank-revealing qr factorization
Gu, M., and Eisenstat, S. C · 1996
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A theory of pseudoskeleton approximations
Goreinov, S., Tyrtyshnikov, E., and Zamarashkin, N · 1997
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Numerical Linear Algebra
Trefethen, L. N., and Bau, D · 1997
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Approximate nearest neighbors: Towards removing the curse of dimensionality
Indyk, P., and Motwani, R · 1998
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Approximation of boundary element matrices
Bebendorf, M · 2000
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On the existence and computation of rank-revealing lu factorizations
Pan, C.-T · 2000
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Incomplete cross approximation in the mosaic-skeleton method
Tyrtyshnikov, E · 2000
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Strong rank revealing lu factorizations
Miranian, L., and Gu, M · 2003
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Meszaros/large, lp sequence: large000 to large036
Meszaros, C · 2004
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The adaptive cross approximation algorithm for accelerated method of moments computations of emc problems
Kezhong Zhao, Vouvakis, M. N., and Jin-Fa Lee · 2005
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Matrix approximation and projective clustering via volume sampling
Deshpande, A., Rademacher, L., Vempala, S., and Wang, G · 2006
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Randomized algorithms for the low-rank approximation of matrices
Liberty, E., Woolfe, F., Martinsson, P.-G., Rokhlin, V., and Tygert, M · 2007
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Relative-error $cur$ matrix decompositions
Drineas, P., Mahoney, M. W., and Muthukrishnan, S · 2008
Cited alongside, same era.
A fast randomized algorithm for overdetermined linear least-squares regression
Rokhlin, V., and Tygert, M · 2008
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A fast randomized algorithm for the approximation of matrices
Woolfe, F., Liberty, E., Rokhlin, V., and Tygert, M · 2008
Cited alongside, same era.
Twice-ramanujan sparsifiers
Batson, J. D., Spielman, D. A., and Srivastava, N · 2009
Cited alongside, same era.
Cur matrix decompositions for improved data analysis
Mahoney, M. W., and Drineas, P · 2009
Cited alongside, same era.
On selecting a maximum volume sub-matrix of a matrix and related problems
Çivril, A., and Magdon-Ismail, M · 2009
Spectral Gap Error Bounds for Improving CUR Matrix Decomposition and the Nyström Method
Anderson, D., Du, S., Mahoney, M., Melgaard, C., Wu, K., and Gu, M · 2015
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Uniform sampling for matrix approximation
Cohen, M. B., Lee, Y. T., Musco, C., Musco, C., Peng, R., and Sidford, A · 2015
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Randomized block krylov methods for stronger and faster approximate singular value decomposition
Musco, C., and Musco, C · 2015
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Random multipliers numerically stabilize gaussian and block gaussian elimination: Proofs and an extension to low-rank approximation
Pan, V. Y., Qian, G., and Yan, X · 2015
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Randomized lu decomposition using sparse projections
Aizenbud, Y., Shabat, G., and Averbuch, A · 2016
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Cited alongside, same era.
Cur from a sparse optimization viewpoint
Bien, J., Xu, Y., and Mahoney, M · 2010
Cited alongside, same era.
Efficient volume sampling for row/column subset selection
Deshpande, A., and Rademacher, L · 2010
Cited alongside, same era.
Near optimal column-based matrix reconstruction
Boutsidis, C., Drineas, P., and Magdon-Ismail, M · 2011
Cited alongside, same era.
Calu: A communication optimal lu factorization algorithm
Grigori, L., Demmel, J. W., and Xiang, H · 2011
Cited alongside, same era.
Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
Halko, N., Martinsson, P. G., and Tropp, J. A · 2011
Cited alongside, same era.
Communication-optimal parallel 2.5d matrix multiplication and lu factorization algorithms
Solomonik, E., and Demmel, J · 2011
Cited alongside, same era.
Drmač, Z., and Gugercin, S · 2016
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A deim induced cur factorization
Sorensen, D. C., and Embree, M · 2016
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An efficient, sparsity-preserving, online algorithm for low-rank approximation
Anderson, D., and Gu, M · 2017
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Low-rank approximation and regression in input sparsity time
Clarkson, K. L., and Woodruff, D. P · 2017
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Numerically safe gaussian elimination with no pivoting
Pan, V. Y., and Zhao, L · 2017
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Fixed-rank approximation of a positive-semidefinite matrix from streaming data
Tropp, J. A., Yurtsever, A., Udell, M., and Cevher, V · 2017
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Efficient algorithms for cur and interpolative matrix decompositions
Voronin, S., and Martinsson, P.-G · 2017
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Randomized lu decomposition
Shabat, G., Shmueli, Y., Aizenbud, Y., and Averbuch, A · 2018
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Low-rank approximation in the frobenius norm by column and row subset selection, 2019
Cortinovis, A., and Kressner, D · 2019
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Streaming low-rank matrix approximation with an application to scientific simulation
Tropp, J. A., Yurtsever, A., Udell, M., and Cevher, V · 2019
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Efficient spectrum-revealing cur matrix decomposition
Chen, C., Gu, M., Zhang, Z., Zhang, W., and Yu, Y · 2020
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Derezinski, M., Khanna, R., and Mahoney, M. W · 2020
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Lowrankapprox,jl: v0.4.3
Ho, K., Olver, S., Kelman, T., Jarlebring, E., TagBot, J., and Slevinsky, M · 2020
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Randomized numerical linear algebra: Foundations and algorithms
Martinsson, P.-G., and Tropp, J. A · 2020
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Determinantal point processes in randomized numerical linear algebra
Dereziński, M., and Mahoney, M · 2021
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