On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems
文献类型：期刊论文
| 作者 | Bai, Zhong-Zhi2 ; Golub, Gene H.3; Ng, Michael K.1
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| 刊名 | LINEAR ALGEBRA AND ITS APPLICATIONS
 |
| 出版日期 | 2008-01-15 |
| 卷号 | 428期号:2-3页码:413-440 |
| 关键词 | Hermitian matrix skew-Hermitian matrix inexact iterations conjugate gradient (CG) method Lanczos method conjugate gradient for normal equations (CGNE) method |
| ISSN号 | 0024-3795 |
| DOI | 10.1016/j.laa.2007.02.018 |
| 英文摘要 | We study theoretical properties of two inexact Hermitian/skew-Hermitian splitting (IHSS) iteration methods for the large sparse non-Hermitian positive definite system of linear equations. In the inner iteration processes, we employ the conjugate gradient (CG) method to solve the linear systems associated with the Hermitian part, and the Lanczos or conjugate gradient for normal equations (CGNE) method to solve the linear systems associated with the skew-Hermitian part, respectively, resulting in IHSS(CG, Lanczos) and IHSS(CG, CGNE) iteration methods, correspondingly. Theoretical analyses show that both IHSS(CG, Lanczos) and IHSS(CG, CGNE) converge unconditionally to the exact solution of the non-Hermitian positive definite linear system. Moreover, their contraction factors and asymptotic convergence rates are dominantly dependent on the spectrum of the Hermitian part, but are less dependent on the spectrum of the skew-Hermitian part, and are independent of the eigenvectors of the matrices involved. Optimal choices of the inner iteration steps in the IHSS(CG, Lanczos) and IHSS(CG, CGNE) iterations are discussed in detail by considering both global convergence speed and overall computation workload, and computational efficiencies of both inexact iterations are analyzed and compared deliberately. (c) 2007 Elsevier Inc. All rights reserved. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000252172800003 |
| 出版者 | ELSEVIER SCIENCE INC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/6826]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Ng, Michael K. |
| 作者单位 | 1.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100080, Peoples R China 3.Stanford Univ, Dept Comp Sci, Sci Comp & Computat Math Program, Stanford, CA 94305 USA |
| 推荐引用方式 GB/T 7714 | Bai, Zhong-Zhi,Golub, Gene H.,Ng, Michael K.. On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2008,428(2-3):413-440. |
| APA | Bai, Zhong-Zhi,Golub, Gene H.,&Ng, Michael K..(2008).On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems.LINEAR ALGEBRA AND ITS APPLICATIONS,428(2-3),413-440. |
| MLA | Bai, Zhong-Zhi,et al."On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems".LINEAR ALGEBRA AND ITS APPLICATIONS 428.2-3(2008):413-440. |
入库方式： OAI收割
来源：数学与系统科学研究院
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