On convergence of greedy block nonlinear Kaczmarz methods with momentum
Numerical Analysis
2025-03-14 v1 Numerical Analysis
Abstract
In this paper, for solving nonlinear systems we propose two pseudoinverse-free greedy block methods with momentum by combining the residual-based weighted nonlinear Kaczmarz and heavy ball methods. Without the full column rank assumptions on Jacobi matrices of nonlinear systems, we provide a thorough convergence analysis, and derive upper bounds for the convergence rates of the new methods. Numerical experiments demonstrate that the proposed methods with momentum are much more effective than the existing ones.
Keywords
Cite
@article{arxiv.2503.10172,
title = {On convergence of greedy block nonlinear Kaczmarz methods with momentum},
author = {Naiyu Jiang and Wendi Bao and Lili Xing and Weiguo Li},
journal= {arXiv preprint arXiv:2503.10172},
year = {2025}
}