Randomized Kaczmarz methods fail to be forward stable but can be stabilized by iterative refinement to recover high-accuracy solutions for ill-conditioned linear systems.
and Meier, Maike and Nakatsukasa, Yuji , copyright =
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sGKS matches standard GKS reconstruction quality for Tikhonov regularization while reducing costs via sketching for QR factorizations and skipping reorthogonalization, with theoretical guarantees on iterate identity and quasi-optimal residuals.
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Numerical Instabilities in the Kaczmarz Method and Stabilization by Iterative Refinement
Randomized Kaczmarz methods fail to be forward stable but can be stabilized by iterative refinement to recover high-accuracy solutions for ill-conditioned linear systems.
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A Sketched Generalized Krylov Subspace Method for Large-Scale Regularization
sGKS matches standard GKS reconstruction quality for Tikhonov regularization while reducing costs via sketching for QR factorizations and skipping reorthogonalization, with theoretical guarantees on iterate identity and quasi-optimal residuals.