Regularized HSS iteration methods for stabilized saddle-point problems

doi:10.1093/imanum/dry046

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	Regularized HSS iteration methods for stabilized saddle-point problems
	Bai, Zhong-Zhi
刊名	IMA JOURNAL OF NUMERICAL ANALYSIS
	2019-10-01
卷号	39 期号:4 页码:1888-1923
关键词	stabilized saddle-point problem Hermitian and skew-Hermitian splitting stationary iteration method inexact implementation preconditioning convergence
ISSN号	0272-4979
DOI	10.1093/imanum/dry046
英文摘要	We extend the regularized Hermitian and skew-Hermitian splitting (RHSS) iteration methods for standard saddle-point problems to stabilized saddle-point problems and establish the corresponding unconditional convergence theory for the resulting methods. Besides being used as stationary iterative solvers, this class of RHSS methods can also be used as preconditioners for Krylov subspace methods. It is shown that the eigenvalues of the corresponding preconditioned matrix are clustered at a small number of points in the interval when the iteration parameter is close to and, furthermore, they can be clustered near and when the regularization matrix is appropriately chosen. Numerical results on stabilized saddle-point problems arising from finite element discretizations of an optimal boundary control problem and of a Cahn-Hilliard image inpainting problem, as well as from the Gauss-Newton linearization of a nonlinear image restoration problem, show that the RHSS iteration method significantly outperforms the Hermitian and skew-Hermitian splitting iteration method in iteration counts and computing times when they are used either as linear iterative solvers or as matrix splitting preconditioners for Krylov subspace methods, and optimal convergence behavior can be achieved when using inexact variants of the proposed RHSS preconditioners.
资助项目	National Natural Science Foundation, P. R. China[11671393]
WOS研究方向	Mathematics
语种	英语
出版者	OXFORD UNIV PRESS
WOS记录号	WOS:000491253300010
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/35802]
专题	计算数学与科学工程计算研究所
通讯作者	Bai, Zhong-Zhi
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, POB 2719, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi. Regularized HSS iteration methods for stabilized saddle-point problems[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2019,39(4):1888-1923.
APA	Bai, Zhong-Zhi.(2019).Regularized HSS iteration methods for stabilized saddle-point problems.IMA JOURNAL OF NUMERICAL ANALYSIS,39(4),1888-1923.
MLA	Bai, Zhong-Zhi."Regularized HSS iteration methods for stabilized saddle-point problems".IMA JOURNAL OF NUMERICAL ANALYSIS 39.4(2019):1888-1923.