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arXiv · 2507.13855

A stochastic column-block gradient descent method for solving nonlinear systems of equations

Naiyu Jiang·Wendi Bao·Lili Xing·Weiguo Li
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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.

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Naiyu Jiang, Wendi Bao, Lili Xing, Weiguo Li. 2025-07-18. A stochastic column-block gradient descent method for solving nonlinear systems of equations. https://arxiv.org/abs/2507.13855

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