SIAM Review, Volume 65, Issue 4, Page 1137-1151, November 2023.
We present Cimmino's reflection algorithm for the numerical solution of linear systems, which starts with an arbitrary point in $\mathbb{R}^n$ that gets reflected with respect to the system's hyperplanes. The centroid of the ensuing collection of points becomes the starting point of the next iteration. We provide error estimates for the convergence at each step. A probabilistic argument is also devised to improve this elegant geometrical algorithm. This subject is an opportunity to show students how linear algebra can interact fruitfully not only with algebra, geometry, and numerical analysis, but also with probability theory and methods.

中文翻译：

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线性系统数值解的反映法

SIAM Review，第 65 卷，第 4 期，第 1137-1151 页，2023 年 11 月。
我们提出了用于线性系统数值解的 Cimmino 反射算法，该算法从 $\mathbb{R}^n$ 中的任意点开始，并通过尊重系统的超平面。随后的点集合的质心成为下一次迭代的起点。我们提供每一步收敛的误差估计。还设计了概率论证来改进这种优雅的几何算法。本课程向学生展示线性代数如何与代数、几何和数值分析以及概率论和方法进行富有成效的互动。