, Volume 98, Issue 1, pp 1-32
Date: 16 Mar 2004

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

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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.

Mathematics Subject Classification: 65F10, 65F50, CR: G1.3
Subsidized by The Special Funds For Major State Basic Research Projects G1999032803
Research supported, in part, by DOE-FC02-01ER4177
Revised version received November 5, 2003