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تسجيل مستخدم جديدQuantile-Based Random Kaczmarz for corrupted linear systems of equations
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نشر من قبل
Stefan Steinerberger
تاريخ النشر
2021
مجال البحث
الهندسة المعلوماتية
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English
تأليف
Stefan Steinerberger
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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).
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