Abstract:

 Based on the normal／skew-Hermitian splitting(NSS) iteration technique for large sparse non-Hermitian and positive definite linear systems, preconditioned normal／skew-Hermitian splitting (PNSS) methods and investigation of their variants are proposed, e.g., the inexact preconditioned normal／skewHermitian splitting (IPNSS) methods. Theoretical analysis shows that the PNSS methods are convergent under some conditions. Also, the computational methods of the optimal choice of the parameter are presented as involved in our iterative schemes and the corresponding minimum values for the upper bound of the iterative spectrums. In the numerical test, we choose incremental unknowns (IUs) and symmetric successive overrelaxation(SSOR) as two types of our precondioners. Numerical results confirm the correctness of the convergence theory and the effectiveness of the proposed methods.

Key words: normal／skew-Hermitian splitting; precondition matrix; non-Hermitian and positive definite linear systems; convergence theory