English

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.

Keywords

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

R2 v1 2026-06-28T11:04:33.023Z