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In this paper, we study matrix scaling and balancing, which are fundamental problems in scientific computing, with a long line of work on them that dates back to the 1960s.
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David T Brown · 1959
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E. E. Osborne · 1960
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Richard Sinkhorn · 1964
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Shmuel Friedland, Chi-Kwong Li, and Hans Schneider · 1988
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Faster scaling algorithms for network problems
Harold N Gabow and Robert E Tarjan · 1989
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A comparative study of algorithms for matrix balancing
Michael H Schneider and Stavros A Zenios · 1990
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Max-balancing weighted directed graphs and matrix scaling
Hans Schneider and Michael H Schneider · 1991
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Solving linear equations with symmetric diagonally dominant matrices by constructing good preconditioners
Pravin M. Vaidya · 1991
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Faster parametric shortest path and minimum-balance algorithms
Neal E Young, Robert E Tarjan, and James B Orlin · 1991
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Rounding errors in algebraic processes
James Hardy Wilkinson · 1994
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On the complexity of nonnegative-matrix scaling
Bahman Kalantari and Leonid Khachiyan · 1996
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On the complexity of matrix balancing
Bahman Kalantari, Leonid Khachiyan, and A Shokoufandeh · 1997
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A nearly m log n m\log n -time solver for SDD linear systems
Ioannis Koutis, Gary L. Miller, and Richard Peng · 2011
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Graph sparsification by effective resistances
Daniel A Spielman and Nikhil Srivastava · 2011
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Runtime guarantees for regression problems
Hui Han Chin, Aleksander Madry, Gary L. Miller, and Richard Peng · 2013
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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A simple, combinatorial algorithm for solving SDD systems in nearly-linear time
Jonathan A. Kelner, Lorenzo Orecchia, Aaron Sidford, and Zeyuan Allen Zhu · 2013
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Navigating central path with electrical flows: From flows to matchings, and back
Aleksander Madry · 2013
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A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents
Nathan Linial, Alex Samorodnitsky, and Avi Wigderson · 1998
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Introductory lectures on convex programming volume i: Basic course
Yu Nesterov · 1998
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On complexity of matrix scaling
Arkadi Nemirovski and Uriel Rothblum · 1999
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Balancing sparse matrices for computing eigenvalues
Tzu-Yi Chen and James W Demmel · 2000
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Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Aharon Ben-Tal and Arkadi Nemirovski · 2001
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Classical deterministic complexity of edmonds’ problem and quantum entanglement
Leonid Gurvits · 2003
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Solving sdd linear systems in nearly m log 1 / 2 n \log^{1/2}n time
Michael B. Cohen, Rasmus Kyng, Gary L. Miller, Jakub W. Pachocki, Richard Peng, Anup B. Rao, and Shen Chen Xu · 2014
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Sparsified cholesky solvers for sdd linear systems
Yin Tat Lee, Richard Peng, and Daniel A Spielman · 2015
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An SDP-based algorithm for linear-sized spectral sparsification
Yin Tat Lee and He Sun · 2015
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Analysis of a classical matrix preconditioning algorithm
Leonard J Schulman and Alistair Sinclair · 2015
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A review of matrix scaling and sinkhorn’s normal form for matrices and positive maps
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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Approximate gaussian elimination for laplacians: Fast, sparse, and simple
Rasmus Kyng and Sushant Sachdeva · 2016
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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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Constructing linear-sized spectral sparsification in almost-linear time
Yin Tat Lee and He Sun · 2017
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Matrix balancing in L p {}_{\mbox{p}} norms: Bounding the convergence rate of osborne’s iteration
Rafail Ostrovsky, Yuval Rabani, and Arman Yousefi · 2017
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