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Matrix scaling is a simple to state, yet widely applicable linear-algebraic problem: the goal is to scale the rows and columns of a given non-negative matrix such that the rescaled matrix has prescribed row and column sums.
Peter Bürgisser, Cole Franks, Ankit Garg, Rafael Oliveira, Michael Walter, and Avi Wigderson · 1910
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Quantum speedup for graph sparsification, cut approximation and laplacian solving
Simon Apers and Ronald de Wolf · 1911
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Telefoonverkeersrekening
J. Kruithof · 1937
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On a least squares adjustment of a sampled frequency table when the expected marginal totals are known
W. Edwards Deming and Frederick F. Stephan · 1940
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A note on approximations to discrete probability distributions
David T. Brown · 1959
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A relationship between arbitrary positive matrices and doubly stochastic matrices
Richard Sinkhorn · 1964
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Discrete Multivariate Analysis: Theory and Practice
Yvonne M. M. Bishop, Stephen E. Fienberg, and Paul W. Holland · 1975
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Scalings of matrices which have prespecified row sums and column sums via optimization
Uriel G. Rothblum and Hans Schneider · 1989
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On the rate of convergence of deterministic and randomized RAS matrix scaling algorithms
Bahman Kalantari and Leonid Khachiyan · 1993
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On the complexity of nonnegative-matrix scaling
Bahman Kalantari and Leonid Khachiyan · 1996
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LAPACK Users’ guide
Edward Anderson, Zhaojun Bai, Christian Bischof, L Susan Blackford, James Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum, Sven Hammarling, Alan McKenney, et al · 1999
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The quantum query complexity of approximating the median and related statistics
Ashwin Nayak and Felix Wu · 1999
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A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents
Nathan Linial, Alex Samorodnitsky, and Avi Wigderson · 2000
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Quantum lower bounds by polynomials
Robert Beals, Harry Buhrman, Richard Cleve, Michele Mosca, and Ronald de Wolf · 2001
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Quantum lower bounds by quantum arguments
Andris Ambainis · 2002
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Negative weights make adversaries stronger
Peter Høyer, Troy Lee, and Robert Špalek · 2007
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A strong direct product theorem for quantum query complexity
Troy Lee and Jérémie Roland · 2013
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Sparsified Cholesky solvers for SDD linear systems, 2015
Yin Tat Lee, Richard Peng, and Daniel A. Spielman · 2015
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A review of matrix scaling and Sinkhorn’s normal form for matrices and positive maps, 2016
Martin Idel · 2016
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Sparsified Cholesky and multigrid solvers for connection Laplacians
Rasmus Kyng, Yin Tat Lee, Richard Peng, Sushant Sachdeva, and Daniel A. Spielman · 2016
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Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration
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On the complexity of general matrix scaling and entropy minimization via the RAS algorithm
B. Kalantari, I. Lari, F. Ricca, and B. Simeone · 2008
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Quantum Algorithms for Matrix Scaling and Matrix Balancing
Joran van Apeldoorn, Sander Gribling, Yinan Li, Harold Nieuwboer, Michael Walter, and Ronald de Wolf · 2011
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Quantum query complexity of state conversion
Troy Lee, Rajat Mittal, Ben Reichardt, Robert Špalek, and Mario Szegedy · 2011
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Marco Cuturi · 2013
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Jason Altschuler, Jonathan Niles-Weed, and Philippe Rigollet · 2017
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Much faster algorithms for matrix scaling
Zeyuan Allen-Zhu, Yuanzhi Li, Rafael Oliveira, and Avi Wigderson · 2017
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Matrix scaling and balancing via box constrained Newton’s method and interior point methods
Michael B. Cohen, Aleksander Madry, Dimitris Tsipras, and Adrian Vladu · 2017
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Operator scaling: theory and applications
Ankit Garg, Leonid Gurvits, Rafael Oliveira, and Avi Wigderson · 2019
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Better and simpler error analysis of the Sinkhorn–Knopp algorithm for matrix scaling
Deeparnab Chakrabarty and Sanjeev Khanna · 2020
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