BIT Numerical Mathematics

, Volume 48, Issue 1, pp 139–162 | Cite as

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

  • Xiaonan Wu
  • Gene H. Golub
  • José A. Cuminato
  • Jin Yun Yuan


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.

Key words

symmetric and triangular (ST) decomposition nonsymmetric system symmetric-positive-definite and triangular decomposition symmetric and positive definite system indefinite system tridiagonal system 


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Copyright information

© Springer Science + Business Media B.V. 2008

Authors and Affiliations

  • Xiaonan Wu
    • 1
  • Gene H. Golub
    • 2
  • José A. Cuminato
    • 3
  • Jin Yun Yuan
    • 4
  1. 1.Department of MathematicsHong Kong Baptist UniversityKowloon, Hong KongChina
  2. 2.Computer Science DepartmentStanford UniversityStanfordUSA
  3. 3.Departamento de Matemática Aplicada e EstátisticaICMC-São Carlos-USPSão CarlosBrazil
  4. 4.Departamento de Matemática – UFPRCentro PolitécnicoCuritibaBrazil

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