Maximum-weighted matching strategies and the application to symmetric indefinite systems

Abstract

The problem of finding good numerical preprocessing methods for the solution of symmetric indefinite systems is considered. Special emphasis is put on symmetric maximum-weighted matching strategies. The aim is to permute large elements of the matrix to diagonal blocks. Several variants for the block sizes are examined and the accuracies of the solutions are compared. It is shown that maximum-weighted matchings improve the accuracy of sparse direct linear solvers. The use of a strategy called FULL CYCLES results in an accurate and reliable factorization. Numerical experiments validate these conclusions. © Springer-Verlag Berlin Heidelberg 2006.