Good pivots for small sparse matrices
This work addresses an incremental improvement in numerical linear algebra for small-scale sparse matrix computations.
The paper tackled the problem of optimal pivot selection for small sparse matrices up to 8x8 in Gaussian elimination, finding that optimal pivots slightly outperform a popular strategy, and a machine learning-based strategy achieved a small improvement over classical methods.
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.