Symmetric-triangular decomposition and its applications part II: Preconditioners for indefinite systems

Xiaonan WU*, Gene H. Golub, José A. Cuminato, Jin Yun Yuan

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

31 Citations (Scopus)


As an application of the symmetric-triangular (ST) decomposition given by Golub and Yuan (2001) and Strang (2003), three block ST preconditioners are discussed here for saddle point problems. All three preconditioners transform saddle point problems into a symmetric and positive definite system. The condition number of the three symmetric and positive definite systems are estimated. Therefore, numerical methods for symmetric and positive definite systems can be applied to solve saddle point problems indirectly. A numerical example for the symmetric indefinite system from the finite element approximation to the Stokes equation is given. Finally, some comments are given as well.

Original languageEnglish
Pages (from-to)139-162
Number of pages24
JournalBIT Numerical Mathematics
Issue number1
Publication statusPublished - Mar 2008

Scopus Subject Areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Indefinite system
  • Nonsymmetric system
  • Symmetric and positive definite system
  • Symmetric and triangular (ST) decomposition
  • Symmetric-positive-definite and triangular decomposition
  • Tridiagonal system


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