We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the deterministic models. The analysis of the expected number of iterations needed in the worst case to achieve a desired level of accuracy in the first-order optimality condition provides guidelines for applying sampling and enforcing, with \minor{a} fixed probability, a suitable accuracy in the random approximations. Results of the numerical validation of the algorithms are presented.

翻译：本文针对非线性最小二乘问题及非线性方程组，提出并分析了一类随机不精确高斯-牛顿方法。该方法通过采用适当的采样策略，对确定性模型中涉及的矩阵构建随机模型。通过对最坏情况下达到一阶最优性条件所需精度的期望迭代次数进行分析，为采样策略的应用提供了指导，并确保以固定概率在随机近似中达到合适的精度。文中同时给出了算法的数值验证结果。