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

  • Authors:

  • Zhong-Zhi Bai;Gene H. Golub;Jian-Yu Pan

  • Affiliations:

  • Institute of Computational Mathematics and Scientific/Engineering Computing, State Key Laboratory of Scientific/Engineering Computing, Acad. Math. and Sys. Sci., Ch. Acad. Sci., Beijing, People&#x ...;Department of Computer Science, Stanford University, Scientific Computing and Computational Mathematics Program, Acad. Math. and Sys. Sci., Ch. Acad. Sci., CA 94305-9025, Stanford, USA;Institute of Computational Mathematics and Scientific/Engineering Computing, State Key Laboratory of Scientific/Engineering Computing, Acad. Math. and Sys. Sci., Ch. Acad. Sci., Beijing, People&#x ...

  • Venue:
  • Numerische Mathematik
  • Year:
  • 2004

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Abstract

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.