We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and inexact Newton methods for nonlinear systems of equations. 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 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开发并分析了随机非精确高斯-牛顿法，针对非线性方程组开发并分析了非精确牛顿法。通过采用适当的采样策略对确定性模型中的矩阵进行随机建模。在最坏情况下达到一阶最优性条件所需精度期望迭代次数的分析，为采样策略的应用以及以固定概率保证随机近似达到适当精度提供了理论指导。文中同时给出了算法的数值验证结果。