论文标题
基于分位数的随机稀疏kaczmarz用于损坏和嘈杂的线性系统
Quantile-based Random Sparse Kaczmarz for Corrupted and Noisy Linear Systems
论文作者
论文摘要
随机的Kaczmarz方法以及其最近开发的变体已成为处理大型线性系统的流行工具。但是，当线性系统受到重型腐败影响时，这些方法通常无法融合，这在许多实际应用中很常见。在这项研究中，我们通过利用分位数来检测腐败，开发了具有线性收敛的随机稀疏kaczmarz方法的新变体。此外，我们将平均块技术纳入了实现并行计算和加速的建议方法中。最后，通过广泛的数值实验说明了所提出的算法非常有效。
The randomzied Kaczmarz method, along with its recently developed variants, has become a popular tool for dealing with large-scale linear systems. However, these methods usually fail to converge when the linear systems are affected by heavy corruptions, which are common in many practical applications. In this study, we develop a new variant of the randomzied sparse Kaczmarz method with linear convergence guarantees, by making use of a quantile technique to detect corruptions. Moreover, we incorporate averaged block technique into the proposed method to achieve parallel computation and acceleration. Finally, the proposed algorithms are illustrated to be very efficient through extensive numerical experiments.
