New Pivot Selection for Sparse Symmetric Indefinite Factorization
For numerical linear algebra practitioners, this offers an improved method for factorizing sparse indefinite matrices, though it is an incremental improvement over existing techniques.
The paper proposes a new pivot selection technique for sparse symmetric indefinite factorization that balances sparsity and numerical stability, producing sparser factors than the MA57 solver while maintaining stability.
We propose a new pivot selection technique for symmetric indefinite factorization of sparse matrices. Such factorization should maintain both sparsity and numerical stability of the factors, both of which depend solely on the choices of the pivots. Our method is based on the minimum degree algorithm and also considers the stability of the factors at the same time. Our experiments show that our method produces factors that are sparser than the factors computed by MA57 and are stable.