标题： 一种用于求解非线性方程组的随机列块梯度下降方法 显示英文标题

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

摘要： 在本文中，我们提出了一种新的随机列块梯度下降方法来求解非线性方程组。 它具有下降方向，并通过一个优化问题获得近似最优步长。 我们提供了详尽的收敛性分析，并推导了新方法的收敛速率的上界。 数值实验表明，所提出的方法优于现有方法。 显示英文摘要

摘要： 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.