Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantile-Based Random Kaczmarz for corrupted linear systems of equations   We consider linear systems $Ax = b$ where $A \in \mathbb{R}^{m \times n}$
consists of normalized rows, $\|a_i\|_{\ell^2} = 1$, and where up to $\beta m$
entries of $b$ have been corrupted (possibly by arbitrarily large numbers).
Haddock, Needell, Rebrova and Swartworth propose a quantile-based Random
Kaczmarz method and show that for certain random matrices $A$ it converges with
high likelihood to the true solution. We prove a deterministic version by
constructing, for any matrix $A$, a number $\beta_A$ such that there is
convergence for all perturbations with $\beta < \beta_A$. Assuming a random
matrix heuristic, this proves convergence for tall Gaussian matrices with up to
$\sim 0.5\%$ corruption (a number that can likely be improved).

23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn