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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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.
-
Accelerated PMHSS iteration methods for complex symmetric linear systems
Zheng, Qing-Qing | Ma, Chang-FengNumerical Algorithms, Vol. 73 (2016), Iss. 2 P.501
https://doi.org/10.1007/s11075-016-0105-z [Citations: 22] -
Parameterized QHSS Iteration Method and Its Variants for Non-Hermitian Positive Definite Linear Systems of Strong Skew-Hermitian Parts
Li, Xu | Feng, Jian-ShengCommunications on Applied Mathematics and Computation, Vol. (2024), Iss.
https://doi.org/10.1007/s42967-024-00379-w [Citations: 0] -
A two‐step matrix splitting iteration paradigm based on one single splitting for solving systems of linear equations
Bai, Zhong‐Zhi
Numerical Linear Algebra with Applications, Vol. 31 (2024), Iss. 3
https://doi.org/10.1002/nla.2510 [Citations: 9] -
Preconditioned HSS iteration method and its non-alternating variant for continuous Sylvester equations
Li, Xu | Huo, Hai-Feng | Yang, Ai-LiComputers & Mathematics with Applications, Vol. 75 (2018), Iss. 4 P.1095
https://doi.org/10.1016/j.camwa.2017.10.028 [Citations: 4] -
On the m-step two-parameter generalized Hermitian and skew-Hermitian splitting preconditioning method
Bastani, Mehdi | Salkuyeh, Davod KhojastehAfrika Matematika, Vol. 28 (2017), Iss. 7-8 P.999
https://doi.org/10.1007/s13370-017-0489-5 [Citations: 0] -
A non-alternating preconditioned HSS iteration method for non-Hermitian positive definite linear systems
Wu, Yu-Jiang | Li, Xu | Yuan, Jin-YunComputational and Applied Mathematics, Vol. 36 (2017), Iss. 1 P.367
https://doi.org/10.1007/s40314-015-0231-6 [Citations: 14] -
On preconditioned generalized shift-splitting iteration methods for saddle point problems
Cao, Yang | Miao, Shu-Xin | Ren, Zhi-RuComputers & Mathematics with Applications, Vol. 74 (2017), Iss. 4 P.859
https://doi.org/10.1016/j.camwa.2017.05.031 [Citations: 18] -
A Generalized HSS Iteration Method for Continuous Sylvester Equations
Li, Xu | Wu, Yu-Jiang | Yang, Ai-Li | Yuan, Jin-YunJournal of Applied Mathematics, Vol. 2014 (2014), Iss. P.1
https://doi.org/10.1155/2014/578102 [Citations: 2] -
Two-parameter generalized Hermitian and skew-Hermitian splitting iteration method
Aghazadeh, N. | Khojasteh Salkuyeh, D. | Bastani, M.International Journal of Computer Mathematics, Vol. 93 (2016), Iss. 7 P.1119
https://doi.org/10.1080/00207160.2015.1019873 [Citations: 10] -
Parameterized preconditioned Hermitian and skew-Hermitian splitting iteration method for saddle-point problems
Li, Xu | Yang, Ai-Li | Wu, Yu-JiangInternational Journal of Computer Mathematics, Vol. 91 (2014), Iss. 6 P.1224
https://doi.org/10.1080/00207160.2013.829216 [Citations: 17]