Generalized Preconditioned Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive-Definite Linear Systems
Year: 2012
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 4 : pp. 404–417
Abstract
In this paper, a generalized preconditioned Hermitian and skew-Hermitian splitting (GPHSS) iteration method for a non-Hermitian positive-definite matrix is studied, which covers standard Hermitian and skew-Hermitian splitting (HSS) iteration and also many existing variants. Theoretical analysis gives an upper bound for the spectral radius of the iteration matrix. From practical point of view, we have analyzed and implemented inexact generalized preconditioned Hermitian and skew-Hermitian splitting (IGPHSS) iteration, which employs Krylov subspace methods as its inner processes. Numerical experiments from three-dimensional convection-diffusion equation show that the GPHSS and IGPHSS iterations are efficient and competitive with standard HSS iteration and AHSS iteration.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1201-m3209
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 4 : pp. 404–417
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Hermitian and skew-Hermitian splitting Iteration method Inner iteration.