A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Preconditioning Highly Indefinite and Nonsymmetric Matrices
SIAM Journal on Scientific Computing
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
MA57---a code for the solution of sparse symmetric definite and indefinite systems
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
An out-of-core sparse symmetric-indefinite factorization method
ACM Transactions on Mathematical Software (TOMS)
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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.