arXiv:2006.01623cs.SC
Good pivots for small sparse matrices
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Abstract
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.
The authors were already working on other small-matrix optimizations. They have a 2020 preprint about choosing good pivots for up to 8x8 matrices. https://arxiv.org/abs/2006.01623
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