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We present a Projection onto Convex Sets (POCS) type algorithm for solving systems of linear equations.
Angenäherte auflösung von systemen linearer gleichungen
S. Kaczmarz · 1937
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Strong underrelaxation in Kaczmarz’s method for inconsistent systems
Y. Censor, P.P.B. Eggermont, and D. Gordon · 1983
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The Mathematics of Computerized Tomography
F. Natterer · 1986
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Applications of convex projection theory to image recovery in tomography and related areas
K. M. Sezan and H. Stark · 1987
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On the acceleration of Kaczmarz’s method for inconsistent linear systems
M. Hanke and W. Niethammer · 1990
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New variants of the POCS method using affine subspaces of finite codimension, with applications to irregular sampling
C. Cenker, H.G. Feichtinger, M. Mayer, H. Steier, and T. Strohmer · 1992
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Algebraic reconstruction techniques can be made computationally efficient
G.T. Herman and L.B. Meyer · 1993
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A Kaczmarz-based approach to nonperiodic sampling on unions of rectangular lattices
H. G. Feichtinger and T. Strohmer · 1995
Cited alongside, same era.
The rate of convergence for the method of alternating projections
F. Deutsch and H. Hundal · 1997
Cited alongside, same era.
On the rate of convergence of the alternating projection method in finite dimensional spaces
A. Galàntai · 2005
Cited alongside, same era.
A randomized solver for linear systems with exponential convergence
T. Strohmer and R. Vershynin · 2006
Cited alongside, same era.
A randomized Kaczmarz algorithm with exponential convergence
T. Strohmer and R. Vershynin · 2009
Cited alongside, same era.
Semi-convergence and relaxation parameters for a class of SIRT algorithms
T. Elfving, T. Nikazad, and P. C. Hansen · 2010
Randomized methods for linear constraints: Convergence rates and conditioning
D. Leventhal and A.S. Lewis · 2010
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Randomized Kaczmarz solver for noisy linear systems
D. Needell · 2010
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Paved with good intentions: Analysis of a randomized block kaczmarz method
D. Needell and J. A. Tropp · 2012
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Two-subspace projection method for coherent overdetermined systems
D. Needell and R. Ward · 2012
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Almost sure convergence for the Kaczmarz algorithm with random measurements
A. Powell and X. Chen · 2012
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Beneath the valley of the noncommutative arithmetic-geometric mean inequality: Conjectures, case studies, and consequences
B. Recht and C. Re · 2012
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Faster least squares approximation
P. Drineas, M.W. Mahoney, S. Muthukrishnan, and T. Sarlós
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