Null-space preconditioners for saddle point systems

Jennifer Pestana, Tyrone Rees

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
48 Downloads (Pure)


The null-space method is a technique that has been used for many years to reduce a saddle point system to a smaller, easier to solve, symmetric positive-definite system. This method can be understood as a block factorization of the system. Here we explore the use of preconditioners based on incomplete versions of a particular null-space factorization, and compare their performance with the equivalent Schur-complement based preconditioners. We also describe how to apply the non-symmetric preconditioners proposed using the conjugate gradient method (CG) with a non-standard inner product. This requires an exact solve with the (1,1) block, and the resulting algorithm is applicable in other cases where Bramble-Pasciak CG is used. We verify the efficiency of the newly proposed preconditioners on a number of test cases from a range of applications.
Original languageEnglish
Pages (from-to)1103-1128
Number of pages26
JournalSIAM Journal on Matrix Analysis and Applications
Issue number3
Early online date18 Aug 2016
Publication statusE-pub ahead of print - 18 Aug 2016


  • preconditioning
  • saddle point systems
  • null-space method
  • Schur complement
  • conjugate gradient method
  • iterative methods
  • linear systems
  • sparse matrices


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