### Uittreksel

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.

Taal | Engels |
---|---|

Artikelnummer | e2173 |

Aantal pagina's | 13 |

Tijdschrift | Numerical Linear Algebra with Applications |

Volume | 25 |

Nummer van het tijdschrift | 5 |

DOI's | |

Status | Gepubliceerd - 1 okt 2018 |

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^{T}factorization without pivoting.

*Numerical Linear Algebra with Applications*,

*25*(5), [e2173]. DOI: 10.1002/nla.2173

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^{T}factorization without pivoting'

*Numerical Linear Algebra with Applications*, vol. 25, nr. 5, e2173. DOI: 10.1002/nla.2173

**Preordering saddle-point systems for sparse LDL ^{T} factorization without pivoting.** / Lungten, Sangye; Schilders, Wil H.A.; Scott, Jennifer A.

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

TY - JOUR

T1 - Preordering saddle-point systems for sparse LDLT factorization without pivoting

AU - Lungten,Sangye

AU - Schilders,Wil H.A.

AU - Scott,Jennifer A.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - 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 LDLT 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.

AB - 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 LDLT 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.

KW - Fill-reducing ordering

KW - LDLfactorization

KW - Saddle-point systems

KW - Sparse symmetric indefinite matrices

UR - http://www.scopus.com/inward/record.url?scp=85044428405&partnerID=8YFLogxK

U2 - 10.1002/nla.2173

DO - 10.1002/nla.2173

M3 - Article

VL - 25

JO - Numerical Linear Algebra with Applications

T2 - Numerical Linear Algebra with Applications

JF - Numerical Linear Algebra with Applications

SN - 1070-5325

IS - 5

M1 - e2173

ER -

^{T}factorization without pivoting. Numerical Linear Algebra with Applications. 2018 okt 1;25(5). e2173. Beschikbaar vanaf, DOI: 10.1002/nla.2173