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The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices.
The approximation of one matrix by another of lower rank
Carl Eckart and Gale Young · 1936
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Numerical linear algebra
William Kahan · 1966
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The Hat matrix in regression and ANOVA
David C. Hoaglin and Roy E. Welsch · 1978
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On the early history of the singular value decomposition
G. W. Stewart · 1993
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Matrix computations
Gene H. Golub and Charles F. Van Loan · 1996
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Efficient algorithms for computing a strong rank-revealing QR factorization
Ming Gu and Stanley C. Eisenstat · 1996
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Pseudo-skeleton approximations by matrices of maximal volume
S.A. Goreinov, N.L. Zamarashkin, and E.E. Tyrtyshnikov · 1997
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Algorithm 782: Codes for rank-revealing QR factorizations of dense matrices
C. H. Bischof and Gregorio Quintana-Ortí · 1998
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Computing rank-revealing QR factorizations of dense matrices
C. H. Bischof and Gregorio Quintana-Ortí · 1998
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Matrix Algorithms Volume 1: Basic Decompositions
G.W. Stewart · 1998
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Utv tools: Matlab templates for rank-revealing utv decompositions
Ricardo D Fierro, Per Christian Hansen, and Peter Søren Kirk Hansen · 1999
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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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On the compression of low rank matrices
H. Cheng, Z. Gimbutas, P.G. Martinsson, and V. Rokhlin · 2005
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On the Nyström method for approximating a Gram matrix for improved kernel-based learning
P. Drineas and M. W. Mahoney · 2005
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Approximate nearest neighbors and the fast johnson-lindenstrauss transform
Nir Ailon and Bernard Chazelle · 2006
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Fast Monte Carlo algorithms for matrices. II. Computing a low-rank approximation to a matrix
Petros Drineas, Ravi Kannan, and Michael W. Mahoney · 2006
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A randomized algorithm for the approximation of matrices
Per-Gunnar Martinsson, Vladimir Rokhlin, and Mark Tygert · 2006
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On interpolation and integration in finite-dimensional spaces of bounded functions
P.G. Martinsson, V. Rokhlin, and M. Tygert · 2006
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Improved approximation algorithms for large matrices via random projections
Tamas Sarlos · 2006
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Randomized algorithms for the low-rank approximation of matrices
Edo Liberty, Franco Woolfe, Per-Gunnar Martinsson, Vladimir Rokhlin, and Mark Tygert · 2007
Cited alongside, same era.
Relative-error C U R CUR matrix decompositions
Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan · 2008
Cited alongside, same era.
A fast randomized algorithm for the approximation of matrices
Franco Woolfe, Edo Liberty, Vladimir Rokhlin, and Mark Tygert · 2008
Cited alongside, same era.
An improved approximation algorithm for the column subset selection problem
Christos Boutsidis, Michael W Mahoney, and Petros Drineas · 2009
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Accelerated Dense Random Projections
E. Liberty · 2009
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Cur matrix decompositions for improved data analysis
Michael W Mahoney and Petros Drineas · 2009
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Sketching as a tool for numerical linear algebra
David P. Woodruff · 2014
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True blas-3 performance qrcp using random sampling, 2015
J. Duersch and M. Gu · 2015
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Subspace iteration randomization and singular value problems
M. Gu · 2015
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Blocked rank-revealing qr factorizations: How randomized sampling can be used to avoid single-vector pivoting, 2015
P.G. Martinsson · 2015
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A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices., 2015
P.G. Martinsson and S. Voronin · 2015
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Randomized block krylov methods for stronger and faster approximate singular value decomposition
Cameron Musco and Christopher Musco · 2015
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A randomized algorithm for principal component analysis
Vladimir Rokhlin, Arthur Szlam, and Mark Tygert · 2009
Cited alongside, same era.
An algorithm for the principal component analysis of large data sets
Nathan Halko, Per-Gunnar Martinsson, Yoel Shkolnisky, and Mark Tygert · 2011
Cited alongside, same era.
Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
Nathan Halko, Per-Gunnar Martinsson, and Joel A. Tropp · 2011
Cited alongside, same era.
Randomized algorithms for matrices and data
Michael W Mahoney · 2011
Cited alongside, same era.
A randomized algorithm for the decomposition of matrices
Per-Gunnar Martinsson, Vladimir Rokhlin, and Mark Tygert · 2011
Cited alongside, same era.
Fast approximation of matrix coherence and statistical leverage
Petros Drineas, Malik Magdon-Ismail, Michael W Mahoney, and David P Woodruff · 2012
Cited alongside, same era.
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Randomized algorithms for low-rank matrix factorizations: sharp performance bounds
Rafi Witten and Emmanuel Candes · 2015
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Fast randomized svd, 2016
Inc. Facebook · 2016
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Matrix factorizations at scale: A comparison of scientific data analytics in spark and C + + MPI using three case studies
A. Gittens, A. Devarakonda, E. Racah, M. Ringenburg, L. Gerhardt, J. Kottalam, J. Liu, K. Maschhoff, S. Canon, J. Chhugani, P. Sharma, J. Yang, J. Demmel, J. Harrell, V. Krishnamurthy, M. W. Mahoney, and Prabhat · 2016
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Revisiting the nyström method for improved large-scale machine learning
Alex Gittens and Michael W. Mahoney · 2016
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Randomized methods for matrix computations and analysis of high dimensional data
Per-Gunnar Martinsson · 2016
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Randomized clustered nystrom for large-scale kernel machines, 2016
Farhad Pourkamali-Anaraki and Stephen Becker · 2016
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A deim induced cur factorization
Danny C Sorensen and Mark Embree · 2016
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randUTV: A blocked randomized algorithm for computing a rank-revealing UTV factorization
P.G. Martinsson, G. Quintana Orti, and N. Heavner · 2017
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Householder qr factorization with randomization for column pivoting (hqrrp)
P.G. Martinsson, G. Quintana-Ortí, N. Heavner, and R. van de Geijn · 2017
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Lectures on randomized linear algebra
P. Drineas and M.W. Mahoney · 2018
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Randomized methods for matrix computations
Per-Gunnar Martinsson · 2018
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Linear algebra and learning from data
G. Strang · 2019
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