Abstract
In this paper, a generalization of the positive-definite andskew-Hermitian splitting (GPSS) iteration is considered for solvingnon-Hermitian and positive definite systems of linear equations.Theoretical analysis shows that the GPSS method convergesunconditionally to the exact solution of the linear system, with theupper bound of its convergence factor dependent only on the spectrumof the positive-definite splitting matrices. In some situations,this new scheme can outperform the Hermitian and skew-Hermitiansplitting (HSS) method, the positive-definite and skew-Hermitiansplitting (PSS) method, and the generalized HSS method (GHSS) andcan be used as an efficient preconditioner. Numerical experimentsusing discretization of convection-diffusion-reaction equations demonstratethe effectiveness of the new method.
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