Strategies for Scaling and Pivoting for Sparse Symmetric Indefinite Problems
Iain Duff, Stéphane Pralet · SIAM Journal on Matrix Analysis and Applications · 2005
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 $1 \times 1$ and $2 \times 2$ 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.