Approximate solution of systems of linear equations

By S. Kaczmarz. 1993

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Federated Optimization in Heterogeneous Networks (2018, methodology): “Our dissimilarity characterization is inspired by the randomized Kaczmarz method for solving linear system of equations (Kaczmarz, 1993; Strohmer & Vershynin, 2009), a similar assumption of which has been used to analyze variants of SGD in other settings (see, e.g., Schmidt & Roux, 2013; Vaswani et…”
KACZMARZ METHODS FOR REGULARIZING NONLINEAR ILL-POSED EQUATIONS I: CONVERGENCE ANALYSIS (2007, methodology): “Therefore, it is the natural counterpart of the Landweber–Kaczmarz iteration [11, 20] for ill–posed problems.”
On the Convergence of Federated Optimization in Heterogeneous Networks (2018, methodology): “Our similarity assumption is inspired by the Kaczmarz method for solving linear system of equations (Kaczmarz, 1993).”
Wiley‐Interscience Series in Discrete Mathematics and Optimization (2011, methodology): “We now discuss an iterative algorithm for solving Ax — b, originally analyzed by Kaczmarzin 1937 [51].”
Wiley‐Interscience Series in Discrete Mathematics and Optimization (2011, methodology): “We now discuss an iterative algorithm for solving Ax — b, originally analyzed by Kaczmarzin 1937 [51].”