KMS Of Academy of mathematics and systems sciences, CAS
| Regularized HSS iteration methods for stabilized saddle-point problems | |
Bai, Zhong-Zhi
| |
| 2019-10-01 | |
| Source Publication | IMA JOURNAL OF NUMERICAL ANALYSIS
 |
| ISSN | 0272-4979 |
| Volume | 39Issue:4Pages:1888-1923 |
| Abstract | 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. |
| Keyword | stabilized saddle-point problem Hermitian and skew-Hermitian splitting stationary iteration method inexact implementation preconditioning convergence |
| DOI | 10.1093/imanum/dry046 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation, P. R. China[11671393] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000491253300010 |
| Publisher | OXFORD UNIV PRESS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/35803 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Bai, Zhong-Zhi |
| Affiliation | 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 |
| Recommended Citation 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. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment