Reducing the amount of pivoting in symmetric indefinite systems

This paper illustrates how the communication due to pivoting in the solution of symmetric indefinite linear systems can be reduced by considering innovative approaches that are different from pivoting strategies implemented in current linear algebra libraries. First a tiled algorithm where pivoting is performed within a tile is described and then an alternative to pivoting is proposed. The latter considers a symmetric randomization of the original matrix using the so-called recursive butterfly matrices. In numerical experiments, we compare the accuracy of tile-wise pivoting and of the randomization approach with the accuracy of the Bunch-Kaufman algorithm