KMS Of Academy of mathematics and systems sciences, CAS
| Modified incomplete orthogonal factorization methods using Givens rotations | |
Bai, Zhong-Zhi ; Yin, Jun-Feng
| |
| 2009-09-01 | |
| Source Publication | COMPUTING
 |
| ISSN | 0010-485X |
| Volume | 86Issue:1Pages:53-69 |
| Abstract | We present a class of new preconditioners based on the incomplete Givens orthogonalization (IGO) methods for solving large sparse systems of linear equations. In the new methods, instead of dropping entries and accepting fill-ins according to the magnitudes of values and the sparsity patterns, we adopt a diagonal compensation strategy, in which the dropped entries are re-used by adding to the main diagonal entries of the same rows of the incomplete upper-triangular factors, possibly after suitable relaxation treatments, so that certain constraints on the preconditioning matrices are further satisfied. This strategy can make the computed preconditioning matrices possess certain desired properties, e.g., having the same weighted row sums as the target matrices. Theoretical analysis shows that these modified incomplete Givens orthogonalization (MIGO) methods can preserve certain useful properties of the original matrix, and numerical results are used to verify the stability, the accuracy, and the efficiency of the MIGO methods employed to precondition the Krylov subspace iteration methods such as GMRES. Both theoretical and numerical studies show that the MIGO methods may have the potential to present high-quality preconditioners for large sparse nonsymmetric matrices. |
| Keyword | Preconditioner Givens rotation Incomplete orthogonal factorization Nonsymmetric matrix |
| DOI | 10.1007/s00607-009-0065-4 |
| Language | 英语 |
| Funding Project | National Basic Research Program[2005CB321702] ; China Outstanding Young Scientist Foundation[10525102] ; National Natural Science Foundation[10471146] |
| WOS Research Area | Computer Science |
| WOS Subject | Computer Science, Theory & Methods |
| WOS ID | WOS:000269926700004 |
| Publisher | SPRINGER WIEN |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/7649 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Bai, Zhong-Zhi |
| Affiliation | Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Bai, Zhong-Zhi,Yin, Jun-Feng. Modified incomplete orthogonal factorization methods using Givens rotations[J]. COMPUTING,2009,86(1):53-69. |
| APA | Bai, Zhong-Zhi,&Yin, Jun-Feng.(2009).Modified incomplete orthogonal factorization methods using Givens rotations.COMPUTING,86(1),53-69. |
| MLA | Bai, Zhong-Zhi,et al."Modified incomplete orthogonal factorization methods using Givens rotations".COMPUTING 86.1(2009):53-69. |
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