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Regularized HSS iteration methods for stabilized saddle-point problems
Bai, Zhong-Zhi
AbstractWe 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.
Keywordstabilized saddle-point problem Hermitian and skew-Hermitian splitting stationary iteration method inexact implementation preconditioning convergence
Funding ProjectNational Natural Science Foundation, P. R. China[11671393]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000491253300010
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Document Type期刊论文
Corresponding AuthorBai, Zhong-Zhi
AffiliationChinese 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
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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.
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