For sparse matrices up to size $8 \times 8$, we determine optimal choices for pivot selection in Gaussian elimination. It turns out that they are slightly better than the pivots chosen by a popular pivot selection strategy, so there is some room for improvement. We then create a pivot selection strategy using machine learning and find that it indeed leads to a small improvement compared to the classical strategy.

中文翻译：

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小稀疏矩阵的良好枢轴

对于大小不超过 $8 \times 8$ 的稀疏矩阵，我们确定了高斯消元中枢轴选择的最佳选择。事实证明，它们比流行的枢轴选择策略选择的枢轴略好，因此还有一些改进的空间。然后，我们使用机器学习创建了一个枢轴选择策略，并发现与经典策略相比，它确实带来了很小的改进。