Numerische Mathematik

, Volume 98, Issue 1, pp 1–32 | Cite as

Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems

  • Zhong-Zhi BaiEmail author
  • Gene H. Golub
  • Jian-Yu Pan


For the positive semidefinite system of linear equations of a block two-by-two structure, by making use of the Hermitian/skew-Hermitian splitting iteration technique we establish a class of preconditioned Hermitian/skew-Hermitian splitting iteration methods. Theoretical analysis shows that the new method converges unconditionally to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameter and the corresponding asymptotic convergence rate are computed exactly. Numerical examples further confirm the correctness of the theory and the effectiveness of the method.


Linear System Unique Solution Linear Equation Theoretical Analysis Convergence Rate 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.State Key Laboratory of Scientific/Engineering ComputingInstitute of Computational Mathematics and Scientific/Engineering ComputingBeijingPeople’s Republic of China
  2. 2.Scientific Computing and Computational Mathematics ProgramDepartment of Computer Science, Stanford UniversityStanfordUSA

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