Abstract
Often in applications ranging from medical imaging and sensor networks to error correction and data science (and beyond), one needs to solve large-scale linear systems in which a fraction of the measurements have been corrupted. We consider solving such large-scale systems of linear equations Ax = b that are inconsistent due to corruptions in the measurement vector b. We develop several variants of iterative methods that converge to the solution of the uncorrupted system of equations, even in the presence of large corruptions. These methods make use of a quantile of the absolute values of the residual vector in determining the iterate update. We present both theoretical and empirical results that demonstrate the promise of these iterative approaches.
Original language | English (US) |
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Pages (from-to) | 605-637 |
Number of pages | 33 |
Journal | SIAM Journal on Matrix Analysis and Applications |
Volume | 43 |
Issue number | 2 |
DOIs | |
State | Published - 2022 |
All Science Journal Classification (ASJC) codes
- Analysis
Keywords
- Kaczmarz method
- corrupted linear systems
- least squares problems
- quantile methods
- stochastic iterative methods