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- W4287748377 abstract "Randomized Kaczmarz is a simple iterative method for finding solutions of linear systems $Ax = b$. We point out that the arising sequence $(x_k)_{k=1}^{infty}$ tends to converge to the solution $x$ in an interesting way: generically, as $k rightarrow infty$, $x_k - x$ tends to the singular vector of $A$ corresponding to the smallest singular value. This has interesting consequences: in particular, the error analysis of Strohmer & Vershynin is optimal. It also quantifies the `pre-convergence' phenomenon where the method initially seems to converge faster. This fact also allows for a fast computation of vectors $x$ for which the Rayleigh quotient $|Ax|/|x|$ is small: solve $Ax = 0$ via Randomized Kaczmarz." @default.
- W4287748377 created "2022-07-26" @default.
- W4287748377 creator A5054778975 @default.
- W4287748377 date "2020-06-30" @default.
- W4287748377 modified "2023-09-24" @default.
- W4287748377 title "Randomized Kaczmarz converges along small singular vectors" @default.
- W4287748377 doi "https://doi.org/10.48550/arxiv.2006.16978" @default.
- W4287748377 hasPublicationYear "2020" @default.
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