Accelerating Random Kaczmarz Algorithm Based on Clustering Information
Numerical Analysis
2015-11-20 v2
Abstract
Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate for the exact solution onto that space to get a new estimate. Many vairants of Kaczmarz algorithms are proposed on how to choose better hyperplanes. Using the property of randomly sampled data in high-dimensional space, we propose an accelerated algorithm based on clustering information to improve block Kaczmarz and Kaczmarz via Johnson-Lindenstrauss lemma. Additionally, we theoretically demonstrate convergence improvement on block Kaczmarz algorithm.
Cite
@article{arxiv.1511.05362,
title = {Accelerating Random Kaczmarz Algorithm Based on Clustering Information},
author = {Yujun Li and Kaichun Mo and Haishan Ye},
journal= {arXiv preprint arXiv:1511.05362},
year = {2015}
}