The generalized HSS method for solving singular linear systems
type: Item
instance of: scholarly article
title: The generalized HSS method for solving singular linear systems
zbMATH Open document ID: 1242.65061
author: Wen Li
author: Yang-Peng Liu
author: Xiao-Fei Peng
published in: Journal of Computational and Applied Mathematics
publication date: 2012-03-19T00:00:00Z
review text: The authors present a new GHSS (generalized Hermitian and skew--Hermitian splitting) method for an iterative solution of the large, sparse, non-Hermitian and singular linear system. They derive the GHSS method starting with a Hermitian and skew-Hermitian splitting of the matrix of the system. This splitting depends on two parameters, while the HSS method uses only one parameter-splitting. The advantage of the GHSS method is that as a result of the splitting it can naturally induce a preconditioner that improve the convergence rate of GMRES. On the other hand, costs less time to converge than GHSS. The authors give and prove sufficient conditions for the GHSS method to be semi-convergent and analyze the quasi-optimal choice of the parameters. Numerical examples are included and the results are discussed.
reviewed by: Drahoslava Janovská
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 6015748
zbMATH Keywords: iterative methods
zbMATH Keywords: non-Hermitian and singular linear system
zbMATH Keywords: Hermitian and skew-Hermitian splitting
zbMATH Keywords: GHSS method
zbMATH Keywords: HSS method
zbMATH Keywords: GMRES
zbMATH Keywords: semi-convergence
zbMATH Keywords: sparse matrices
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.cam.2011.11.020
OpenAlex ID: W2059776418
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DOI: 10.1016/J.CAM.2011.11.020
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description: scientific article; zbMATH DE number 6015748