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Volume 30, Issue 4
Generalized Preconditioned Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive-Definite Linear Systems

Junfeng Yin & Quanyu Dou

DOI: 10.4208/jcm.1201-m3209

J. Comp. Math., 30 (2012), pp. 404-417.

Published online: 2012-08

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  • 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.

  • Keywords

Hermitian and skew-Hermitian splitting, Iteration method, Inner iteration.

  • AMS Subject Headings

65F10, 65F20, 65F30, 65F50.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-30-404, author = {Junfeng Yin and Quanyu Dou}, title = {Generalized Preconditioned Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive-Definite Linear Systems}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1201-m3209}, url = {http://global-sci.org/intro/article_detail/jcm/8439.html} }
TY - JOUR T1 - Generalized Preconditioned Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive-Definite Linear Systems AU - Junfeng Yin & Quanyu Dou JO - Journal of Computational Mathematics VL - 4 SP - 404 EP - 417 PY - 2012 DA - 2012/08 SN - 30 DO - http://doi.org/10.4208/jcm.1201-m3209 UR - https://global-sci.org/intro/article_detail/jcm/8439.html KW - Hermitian and skew-Hermitian splitting, Iteration method, Inner iteration. AB -

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.

Junfeng Yin and Quanyu Dou. (2012). Generalized Preconditioned Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive-Definite Linear Systems. Journal of Computational Mathematics. 30 (4). 404-417. doi:10.4208/jcm.1201-m3209
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