Towards Stable Mixed Pivoting Strategies for the Sequential and Parallel Solution of Sparse Symmetric Indefinite Systems

We consider the direct solution of sparse symmetric indefinite matrices. We develop new pivoting strategies that combine numerical pivoting and perturbation techniques. Then an iterative refinement process uses our approximate factorization to compute a solution. We show that our pivoting strategies are numerically robust, that few steps of iterative refinement are required, and that the factorization is significantly faster than with previous methods. Furthermore, we propose original approaches that are designed for parallel distributed factorization. A key point of our parallel implementation is the cheap and reliable estimation of the growth factor. This estimation is based on an approximation of the off-diagonal entries and does not require any supplementary messages.