The row iterative method is popular in solving the large‐scale ill‐posed problems due to its simplicity and efficiency. In this work we consider the randomized row iterative (RRI) method to tackle this issue. First, we present the semiconvergence analysis of RRI method for the overdetermined and inconsistent system, and derive upper bounds for the noise error propagation in the iteration vectors. To achieve a least squares solution, we then propose an extended version of the RRI (ERRI) method, which in fact can converge in expectation to the solution of the overdetermined or underdetermined, consistent or inconsistent systems. Finally, some numerical examples are given to demonstrate the convergence behaviors of the RRI and ERRI methods for these types of linear system.

中文翻译：

---

随机行迭代方法及其扩展变量的半收敛性分析

行迭代方法由于其简单性和效率而在解决大规模不适问题中很受欢迎。在这项工作中，我们考虑使用随机行迭代（RRI）方法来解决此问题。首先，我们针对超定和不一致的系统提出了RRI方法的半收敛性分析，并得出了迭代向量中噪声误差传播的上限。为了实现最小二乘解，我们然后提出了RRI（ERRI）方法的扩展版本，实际上，它可以收敛于对超定或不确定，一致或不一致的系统的求解。最后，通过数值例子说明了这些类型的线性系统的RRI和ERRI方法的收敛性。