English

Kaczmarz-type inner-iteration preconditioned flexible GMRES methods for consistent linear systems

Numerical Analysis 2021-02-25 v6 Numerical Analysis

Abstract

We propose using greedy and randomized Kaczmarz inner-iterations as preconditioners for the right-preconditioned flexible GMRES method to solve consistent linear systems, with a parameter tuning strategy for adjusting the number of inner iterations and the relaxation parameter. We also present theoretical justifications of the right-preconditioned flexible GMRES for solving consistent linear systems. Numerical experiments on overdetermined and underdetermined linear systems show that the proposed method is superior to the GMRES method preconditioned by NE-SOR inner iterations in terms of total CPU time.

Keywords

Cite

@article{arxiv.2006.10818,
  title  = {Kaczmarz-type inner-iteration preconditioned flexible GMRES methods for consistent linear systems},
  author = {Yi-Shu Du and Ken Hayami and Ning Zheng and Keiichi Morikuni and Jun-Feng Yin},
  journal= {arXiv preprint arXiv:2006.10818},
  year   = {2021}
}
R2 v1 2026-06-23T16:26:55.738Z