Hermitian and normal splitting methods for non-Hermitian positive definite linear systems

In this paper, a Hermitian and normal splitting (HNS) iterative method is proposed for solving non-Hermitian positive definite linear systems arising from convection–diffusion–reaction equations. Theoretical analysis shows that the HNS method converges unconditionally to the exact solution of the linear system. Choices of the parameters are discussed. The corresponding inexact HNS (IHNS) iterative method, which is developed by employing some Krylov subspace methods as its inner process, is studied. Finally, some numerical experiments are presented to demonstrate the effectiveness of the new method.