论文标题
线性方程式损坏系统的基于分位数的迭代方法
Quantile-based Iterative Methods for Corrupted Systems of Linear Equations
论文作者
论文摘要
通常，在从医学成像和传感器网络到错误校正和数据科学（及以后）的应用程序中，需要解决大规模的线性系统，其中测量的一部分已损坏。我们考虑求解线性方程式的如此大规模的系统$ \ mathbf {a} \ mathbf {x} = \ mathbf {b} $由于测量向量$ \ mathbf {b} $中的损坏而导致的不一致。我们开发了几种迭代方法的变体，这些变体即使在存在大型腐败的情况下，它们也会融合到不腐败的方程式系统的解决方案。这些方法在确定迭代更新时利用残差向量的绝对值的分位数。我们提出了理论和经验结果，证明了这些迭代方法的希望。
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 $\mathbf{A}\mathbf{x}=\mathbf{b}$ that are inconsistent due to corruptions in the measurement vector $\mathbf{b}$. 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.
