On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems
文献类型：期刊论文
| 作者 | Bai, Zhong-Zhi1,2
|
| 刊名 | COMPUTING
 |
| 出版日期 | 2010-09-01 |
| 卷号 | 89期号:3-4页码:171-197 |
| 关键词 | Singular linear system Non-Hermitian matrix Positive semidefinite matrix Hermitian and skew-Hermitian splitting Splitting iteration method Semi-convergence Preconditioning matrix Krylov subspace method |
| ISSN号 | 0010-485X |
| DOI | 10.1007/s00607-010-0101-4 |
| 英文摘要 | For the singular, non-Hermitian, and positive semidefinite systems of linear equations, we derive necessary and sufficient conditions for guaranteeing the semi-convergence of the Hermitian and skew-Hermitian splitting (HSS) iteration methods. We then investigate the semi-convergence factor and estimate its upper bound for the HSS iteration method. If the semi-convergence condition is satisfied, it is shown that the semi-convergence rate is the same as that of the HSS iteration method applied to a linear system with the coefficient matrix equal to the compression of the original matrix on the range space of its Hermitian part, that is, the matrix obtained from the original matrix by restricting the domain and projecting the range space to the range space of the Hermitian part. In particular, an upper bound is obtained in terms of the largest and the smallest nonzero eigenvalues of the Hermitian part of the coefficient matrix. In addition, applications of the HSS iteration method as a preconditioner for Krylov subspace methods such as GMRES are investigated in detail, and several examples are used to illustrate the theoretical results and examine the numerical effectiveness of the HSS iteration method served either as a preconditioner for GMRES or as a solver. |
| 语种 | 英语 |
| WOS记录号 | WOS:000280594700003 |
| 出版者 | SPRINGER WIEN |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/9394]  |
| 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 | 1.Guizhou Normal Univ, Sch Math & Comp Sci, Guiyang 550001, Peoples R China 2.Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Bai, Zhong-Zhi. On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems[J]. COMPUTING,2010,89(3-4):171-197. |
| APA | Bai, Zhong-Zhi.(2010).On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems.COMPUTING,89(3-4),171-197. |
| MLA | Bai, Zhong-Zhi."On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems".COMPUTING 89.3-4(2010):171-197. |
入库方式： OAI收割
来源：数学与系统科学研究院
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