Preordering saddle-point systems for sparse LDLT factorization without pivoting

Sangye Lungten, Wil H.A. Schilders, Jennifer A. Scott

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 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.

Taal Engels e2173 13 Numerical Linear Algebra with Applications 25 5 10.1002/nla.2173 Gepubliceerd - 1 okt 2018

Vingerafdruk

Pivoting
Factorization
Pivot
Partitioned Matrix
Indefinite Systems
Block Structure
System of Linear Equations
Linear equations
Permutation
Partition
Numerical Results
Graph in graph theory
Range of data

Citeer dit

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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 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.",
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Preordering saddle-point systems for sparse LDLT factorization without pivoting. / Lungten, Sangye; Schilders, Wil H.A.; Scott, Jennifer A.

In: Numerical Linear Algebra with Applications, Vol. 25, Nr. 5, e2173, 01.10.2018.

TY - JOUR

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

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AU - Schilders,Wil H.A.

AU - Scott,Jennifer A.

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Y1 - 2018/10/1

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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

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