Inertial randomized Kaczmarz algorithms for solving coherent linear systems
Numerical Analysis
2023-06-16 v1 Numerical Analysis
Optimization and Control
Abstract
In this paper, by regarding the two-subspace Kaczmarz method [20] as an alternated inertial randomized Kaczmarz algorithm we present a new convergence rate estimate which is shown to be better than that in [20] under a mild condition. Furthermore, we accelerate the alternated inertial randomized Kaczmarz algorithm and introduce a multi-step inertial randomized Kaczmarz algorithm which is proved to have a faster convergence rate. Numerical experiments support the theory results and illustrate that the multi-inertial randomized Kaczmarz algorithm significantly outperform the two-subspace Kaczmarz method in solving coherent linear systems.
Cite
@article{arxiv.2306.08185,
title = {Inertial randomized Kaczmarz algorithms for solving coherent linear systems},
author = {Songnian He and Ziting Wang and Qiao-Li Dong},
journal= {arXiv preprint arXiv:2306.08185},
year = {2023}
}
Comments
24 pages and 14 figures