GENERALIZED PRECONDITIONED HERMITIAN AND SKEW-HERMITIAN SPLITTING METHODS FOR NON-HERMITIAN POSITIVE-DEFINITE LINEAR SYSTEMS  

作　　者：Junfeng Yin Quanyu Dou 

机构地区：[1]Department of Mathematics,Tongji University,Shanghai 200092,China

出　　处：《Journal of Computational Mathematics》2012年第4期404-417,共14页计算数学（英文）

摘　　要：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 iterations are efficient and competitive with equation show that the GPHSS and IGPHSS standard HSS iteration and AHSS iteration.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 iterations are efficient and competitive with equation show that the GPHSS and IGPHSS standard HSS iteration and AHSS iteration.

关 键 词：Hermitian and skew-Hermitian splitting Iteration method Inner iteration. 

分 类 号：O151.21[理学—数学] TN912.3[理学—基础数学]