Simulated Annealing for Pro le and Fill Reduction of Sparse Matrices

1 2 Summary Simulated annealing can minimize both proole and ll of sparse matrices. We applied these techniques to a number of sparse matrices from the Harwell-Boeing Sparse Matrix Collection. We were able to reduce proole typically to about 80% of that attained by conventional proole minimization techniques (and sometimes much lower), but ll reduction was less successful (85% at best). We present a new algorithm that signiicantly speeds up proole computation during the annealing process. Simulated annealing is, however, still much more time-consuming than conventional techniques and is therefore likely to be useful only in situations where the same sparse matrix is being used repeatedly.