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Block triangular and skew-Hermitian splitting methods for positive-definite linear systems
文献类型：期刊论文
| 作者 | Bai, ZZ ; Golub, GH; Lu, LZ; Yin, JF
|
| 刊名 | SIAM JOURNAL ON SCIENTIFIC COMPUTING
 |
| 出版日期 | 2005 |
| 卷号 | 26期号:3页码:844-863 |
| 关键词 | non-Hermitian matrix positive-definite matrix triangular matrix block triangular matrix Hermitian and skew-Hermitian splitting splitting iteration method |
| ISSN号 | 1064-8275 |
| DOI | 10.1137/S1064827503428114 |
| 英文摘要 | By further generalizing the concept of Hermitian (or normal) and skew-Hermitian splitting for a non-Hermitian and positive-definite matrix, we introduce a new splitting, called positive-definite and skew-Hermitian splitting (PSS), and then establish a class of PSS methods similar to the Hermitian (or normal) and skew-Hermitian splitting (HSS or NSS) method for iteratively solving the positive-definite systems of linear equations. Theoretical analysis shows that the PSS method converges unconditionally to the exact solution of the linear system, with the upper bound of its convergence factor dependent only on the spectrum of the positive-definite splitting matrix and independent of the spectrum of the skew-Hermitian splitting matrix as well as the eigenvectors of all matrices involved. When we specialize the PSS to block triangular ( or triangular) and skew-Hermitian splitting (BTSS or TSS), the PSS method naturally leads to a BTSS or TSS iteration method, which may be more practical and efficient than the HSS and NSS iteration methods. Applications of the BTSS method to the linear systems of block two-by-two structures are discussed in detail. Numerical experiments further show the effectiveness of our new methods. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000227761300006 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/1413]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Bai, ZZ |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100080, Peoples R China 2.Stanford Univ, Dept Comp Sci, Sci Comp & Computat Math Program, Stanford, CA 94305 USA 3.Xiamen Univ, Dept Math, Xiamen 361005, Peoples R China |
| 推荐引用方式 GB/T 7714 | Bai, ZZ,Golub, GH,Lu, LZ,et al. Block triangular and skew-Hermitian splitting methods for positive-definite linear systems[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2005,26(3):844-863. |
| APA | Bai, ZZ,Golub, GH,Lu, LZ,&Yin, JF.(2005).Block triangular and skew-Hermitian splitting methods for positive-definite linear systems.SIAM JOURNAL ON SCIENTIFIC COMPUTING,26(3),844-863. |
| MLA | Bai, ZZ,et al."Block triangular and skew-Hermitian splitting methods for positive-definite linear systems".SIAM JOURNAL ON SCIENTIFIC COMPUTING 26.3(2005):844-863. |
入库方式： OAI收割
来源：数学与系统科学研究院
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