On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix

We consider bipartite matching algorithms for computing permutations of a sparse matrix so that the diagonal of the permuted matrix has entries of large absolute value. We discuss various strategies for this and consider their implementation as computer codes. We also consider scaling techniques to further increase the relative values of the diagonal entries. Numerical experiments show the eeect of the reorderings and the scaling on the solution of sparse equations by a direct method and by an iterative technique. The eeect on preconditioning for iterative methods is also discussed.