A study of pivoting strategies for tough sparse indefinite systems

The performance of a sparse direct solver is dependent upon the pivot sequence that is chosen during the analyse phase. In the case of symmetric indefinite systems, it may be necessary to modify this sequence during the factorization to ensure numerical stability. Delaying pivots can have serious consequences in terms of time as well as the memory and flops required for the factorization and subsequent solves. This study focuses on hard-to-solve sparse symmetric indefinite problems for which standard threshold partial pivoting leads to a large number delayed pivots. We perform a detailed review of pivoting strategies that are aimed at reducing delayed pivots without compromising numerical stability. Extensive numerical experiments are performed on a set of tough problems arising from practical applications.