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Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko, Martinsson, and Tropp, randomized Simultaneous Power Iteration has become the method of choice for approximate singular value decomposition.
Das verfahren der treppeniteration und verwandte verfahren zur lösung algebraischer eigenwertprobleme
Friedrich L. Bauer · 1957
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Symmetric gauge functions and unitarily invariant norms
L. Mirsky · 1960
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Simultaneous iteration method for symmetric matrices
H. Rutishauser · 1970
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A block Lanczos algorithm for computing the q algebraically largest eigenvalues and a corresponding eigenspace of large, sparse, real symmetric matrices
Jane Cullum and W.E. Donath · 1974
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The block Lanczos method for computing eigenvalues
Gene Golub and Richard Underwood · 1977
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On the rates of convergence of the Lanczos and the Block-Lanczos methods
Y. Saad · 1980
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A block Lanczos method for computing the singular values and corresponding singular vectors of a matrix
Gene Golub, Franklin Luk, and Michael Overton · 1981
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Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start
J. Kuczyński and H. Woźniakowski · 1992
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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
Ming Gu and Stanley C. Eisenstat · 1996
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Lloyd N. Trefethen and David Bau · 1997
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Fast Monte Carlo algorithms for finding low-rank approximations
Alan Frieze, Ravi Kannan, and Santosh Vempala · 1998
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Christos H. Papadimitriou, Hisao Tamaki, Prabhakar Raghavan, and Santosh Vempala · 1998
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Clustering large graphs via the singular value decomposition
Petros Drineas, Alan Frieze, Ravi Kannan, Santosh Vempala, and V Vinay · 1999
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J.C. Mason and D.C. Handscomb · 2002
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Improved approximation algorithms for large matrices via random projections
Tamás Sarlós · 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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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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Adaptive sampling and fast low-rank matrix approximation
Amit Deshpande and Santosh Vempala · 2006
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Jure Leskovec, Lada A. Adamic, and Bernardo A. Huberman · 2007
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A randomized algorithm for principal component analysis
Vladimir Rokhlin, Arthur Szlam, and Mark Tygert · 2009
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Numerical Methods for Large Eigenvalue Problems: Revised Edition
Yousef Saad · 2011
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Randomized methods for computing low-rank approximations of matrices
Nathan P Halko · 2012
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Low rank approximation and regression in input sparsity time
Kenneth L. Clarkson and David P. Woodruff · 2013
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Low-distortion subspace embeddings in input-sparsity time and applications to robust linear regression
Michael W Mahoney and Xiangrui Meng · 2013
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OSNAP: Faster numerical linear algebra algorithms via sparser subspace embeddings
Jelani Nelson and Huy L. Nguyen · 2013
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Randomized SVD
Antoine Liutkus · 2014
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