A stochastic column-block gradient descent method for solving nonlinear systems of equations
Numerical Analysis
2025-07-21 v1 Numerical Analysis
Abstract
In this paper, we propose a new stochastic column-block gradient descent method for solving nonlinear systems of equations. It has a descent direction and holds an approximately optimal step size obtained through an optimization problem. We provide a thorough convergence analysis, and derive an upper bound for the convergence rate of the new method. Numerical experiments demonstrate that the proposed method outperforms the existing ones.
Cite
@article{arxiv.2507.13855,
title = {A stochastic column-block gradient descent method for solving nonlinear systems of equations},
author = {Naiyu Jiang and Wendi Bao and Lili Xing and Weiguo Li},
journal= {arXiv preprint arXiv:2507.13855},
year = {2025}
}