The randomized Kaczmarz (RK) method is an iterative method for approximating the least-squares solution of large linear systems of equations. The standard RK method uses sequential updates, making parallel computation difficult. Here, we study a parallel version of RK where a weighted average of independent updates is used. We analyze the convergence of RK with averaging and demonstrate its performance empirically. We show that as the number of threads increases, the rate of convergence improves and the convergence horizon for inconsistent systems decreases.

中文翻译：

---

平均的随机 Kaczmarz

随机化 Kaczmarz (RK) 方法是一种迭代方法，用于逼近大型线性方程组的最小二乘解。标准 RK 方法使用顺序更新，使得并行计算变得困难。在这里，我们研究了 RK 的并行版本，其中使用了独立更新的加权平均值。我们通过平均分析 RK 的收敛性，并凭经验证明其性能。我们表明，随着线程数量的增加，收敛速度提高，不一致系统的收敛范围减少。