Sparse Sampling Kaczmarz-Motzkin Method with Linear Convergence
Numerical Analysis
2022-04-13 v2 Numerical Analysis
Optimization and Control
Abstract
The randomized sparse Kaczmarz method was recently proposed to recover sparse solutions of linear systems. In this work, we introduce a greedy variant of the randomized sparse Kaczmarz method by employing the sampling Kaczmarz-Motzkin method, and prove its linear convergence in expectation with respect to the Bregman distance in the noiseless and noisy cases. This greedy variant can be viewed as a unification of the sampling Kaczmarz-Motzkin method and the randomized sparse Kaczmarz method, and hence inherits the merits of these two methods. Numerically, we report a couple of experimental results to demonstrate its superiority
Cite
@article{arxiv.2101.04807,
title = {Sparse Sampling Kaczmarz-Motzkin Method with Linear Convergence},
author = {Ziyang Yuan and Hui Zhang and Hongxia Wang},
journal= {arXiv preprint arXiv:2101.04807},
year = {2022}
}