Strategies for Scaling and Pivoting for Sparse Symmetric Indefinite Problems

We consider ways of implementing preordering and scaling for symmetric systems and show the effect of using this technique with a multifrontal code for sparse symmetric indefinite systems. After having presented a new method for scaling, we propose a way of using an approximation to a symmetric weighted matching to predefine 1 × 1 and 2 × 2 pivots prior to the ordering and analysis phase. We also present new classes of orderings called "(relaxed) constrained orderings" that mix structural and numerical criteria.