Task-parallel tiled direct solver for dense symmetric indefinite systems

This paper proposes a direct solver for symmetric indefinite linear systems. The program is parallelized via the OpenMP task construct and outperforms existing programs. The proposed solver avoids pivoting, which requires a lot of data movement, during factorization with preconditioning using the symmetric random butterfly transformation. The matrix data layout is tiled after the preconditioning to more efficiently use cache memory during factorization. Given the low-rank property of the input matrices, an adaptive crossing approximation is used to make a low-rank approximation before the update step to reduce the computation load. Iterative refinement is then used to improve the accuracy of the final result. Finally, the performance of the proposed solver is compared to that of various symmetric indefinite linear system solvers to show its superiority.