Conjugate gradient method for rank deficient saddle point problems

Xiaonan WU*, B. P.B. Silva, J. Y. Yuan

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

57 Citations (Scopus)


We propose an alternative iterative method to solve rank deficient problems arising in many real applications such as the finite element approximation to the Stokes equation and computational genetics. Our main contribution is to transform the rank deficient problem into a smaller full rank problem, with structure as sparse as possible. The new system improves the condition number greatly. Numerical experiments suggest that the new iterative method works very well for large sparse rank deficient saddle point problems.

Original languageEnglish
Pages (from-to)139-154
Number of pages16
JournalNumerical Algorithms
Issue number2-4
Publication statusPublished - Apr 2004

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • ABS method
  • Conjugate gradient method
  • Direct projection method
  • Finite element approximation
  • Navier-Stokes equation
  • Preconditioner
  • Rank deficient problem
  • Saddle point problem
  • Sparse scientific computing


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