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


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
Issue number5
Publication statusPublished - 1 Oct 2018


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


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