Randomized Kaczmarz method with adaptive stepsizes for inconsistent linear systems
Numerical Analysis
2023-03-17 v3 Numerical Analysis
Abstract
We investigate the randomized Kaczmarz method that adaptively updates the stepsize using readily available information for solving inconsistent linear systems. A novel geometric interpretation is provided which shows that the proposed method can be viewed as an orthogonal projection method in some sense. We prove that this method converges linearly in expectation to the unique minimum Euclidean norm least-squares solution of the linear system, and provide a tight upper bound for the convergence of the proposed method. Numerical experiments are also given to illustrate the theoretical results.
Cite
@article{arxiv.2301.00176,
title = {Randomized Kaczmarz method with adaptive stepsizes for inconsistent linear systems},
author = {Yun Zeng and Deren Han and Yansheng Su and Jiaxin Xie},
journal= {arXiv preprint arXiv:2301.00176},
year = {2023}
}
Comments
to appear in Numerical Algorithms