### Abstract

This paper focuses on efficiently solving large sparse symmetric indefinite systems of linear equations in saddle-point form using a fill-reducing ordering technique with a direct solver. Row and column permutations partition the saddle-point matrix into a block structure constituting a priori pivots of order 1 and 2. The partitioned matrix is compressed by treating each nonzero block as a single entry, and a fill-reducing ordering is applied to the corresponding compressed graph. It is shown that, provided the saddle-point matrix satisfies certain criteria, a block LDL^{T} factorization can be computed using the resulting pivot sequence without modification. Numerical results for a range of problems from practical applications using a modern sparse direct solver are presented to illustrate the effectiveness of the approach.

Original language | English |
---|---|

Article number | e2173 |

Number of pages | 13 |

Journal | Numerical Linear Algebra with Applications |

Volume | 25 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 Oct 2018 |

### Keywords

- Fill-reducing ordering
- LDLfactorization
- Saddle-point systems
- Sparse symmetric indefinite matrices

## Fingerprint Dive into the research topics of 'Preordering saddle-point systems for sparse LDL<sup>T</sup> factorization without pivoting'. Together they form a unique fingerprint.

## Cite this

^{T}factorization without pivoting.

*Numerical Linear Algebra with Applications*,

*25*(5), [e2173]. https://doi.org/10.1002/nla.2173