Good pivots for small sparse matrices

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.

11 pages

References in corpus (3)

• Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition
• Machine Learning for Mathematical Software
• Learning selection strategies in Buchberger's algorithm