2024/03/28 by Nestor Coria, Coria, Nestor, Jamie Haddock +3 · 1 citation
Economics, Econometrics and Finance · #FOS: Mathematics #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2403.19874
openalex publication_date 2024/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Large-scale systems of linear equations arise in machine learning, medical imaging, sensor networks, and in many areas of data science. When the scale of the systems are extreme, it is common for a fraction of the data or measurements to be corrupted. The Quantile Randomized Kaczmarz (QRK) method is known to converge on large-scale systems of linear equations Ax=b that are inconsistent due to static corruptions in the measurement vector b. We prove that QRK converges even for systems corrupted by time-varying perturbations. Additionally, we prove that QRK converges up to a convergence horizon on systems affected by time-varying noise and corruption. Finally, we utilize Markov's inequality to prove a lower bound on the probability that the largest entries of the QRK residual reveal the time-varying corruption in each iteration. We present numerical experiments which illustrate our theoretical results.