On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations
文献类型：期刊论文
| 作者 | Bai, Zhong-Zhi ; Golub, Gene H.; Ng, Michael K.
|
| 刊名 | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
 |
| 出版日期 | 2007-05-01 |
| 卷号 | 14期号:4页码:319-335 |
| 关键词 | non-Hermitian matrix normal matrix Hermitian matrix skew-Hermitian matrix splitting iteration method successive overrelaxation |
| ISSN号 | 1070-5325 |
| DOI | 10.1002/nla.517 |
| 英文摘要 | We further generalize the technique for constructing the Hermitian/skew-Herrnitian splitting (HSS) iteration method for solving large sparse non-Hermitian positive definite system of linear equations to the normal/skew-Hennitian (NS) splitting obtaining a class of normal/skew-Hermitian splitting (NSS) iteration methods. Theoretical analyses show that the NSS method converges unconditionally to the exact solution of thic system of linear equations. Moreover, we derive an upper bound of the contraction factor of the NSS iteration which is dependent solely on the spectrum of the normal splitting matrix, and is independent of the eigenvectors of the matrices involved. We present a successive-overrelaxation (SOR) acceleration scheme for the NSS iteration, which specifically results in an acceleration scheme for the HSS iteration. Convergence conditions for this SOR scheme are derived under the assumption that the eigenvalues of the corresponding block Jacobi iteration matrix lie in certain regions in the complex plane. A numerical example is used to show that the SOR technique can significantly accelerate the convergence rate of the NSS or the HSS iteration method. Copyright (c) 2006 John Wiley & Sons, Ltd. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000245958400005 |
| 出版者 | JOHN WILEY & SONS LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/4402]  |
| 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, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Bai, Zhong-Zhi,Golub, Gene H.,Ng, Michael K.. On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,2007,14(4):319-335. |
| APA | Bai, Zhong-Zhi,Golub, Gene H.,&Ng, Michael K..(2007).On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations.NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,14(4),319-335. |
| MLA | Bai, Zhong-Zhi,et al."On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations".NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 14.4(2007):319-335. |
入库方式： OAI收割
来源：数学与系统科学研究院
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