Preordering saddle-point systems for sparse LDLT factorization without pivoting

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

Research output: Contribution to journalArticleAcademicpeer-review

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.

Original languageEnglish
Article numbere2173
Number of pages13
JournalNumerical Linear Algebra with Applications
Volume25
Issue number5
DOIs
Publication statusPublished - 1 Oct 2018

Keywords

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

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