KMS Of Academy of mathematics and systems sciences, CAS
| On HSS-based iteration methods for weakly nonlinear systems | |
Bai, Zhong-Zhi ; Yang, Xi
| |
| 2009-12-01 | |
| Source Publication | APPLIED NUMERICAL MATHEMATICS
 |
| ISSN | 0168-9274 |
| Volume | 59Issue:12Pages:2923-2936 |
| Abstract | Based oil separable property of the linear and the nonlinear terms and on the Hermitian and skew-Hermitian splitting of the coefficient matrix, we present the Picard-HSS and the nonlinear HSS-like iteration methods for solving a class of large scale systems of weakly nonlinear equations. The advantage of these methods over the Newton and the Newton-HSS iteration methods is that they do not require explicit construction and accurate computation of the Jacobian matrix, and only need to solve linear sub-systems of constant coefficient matrices. Hence, computational workloads and computer memory may be saved in actual implementations. Under suitable conditions, we establish local convergence theorems for both Picard-HSS and nonlinear HSS-like iteration methods. Numerical implementations show that both Picard-HSS and nonlinear HSS-like iteration methods are feasible, effective, and robust nonlinear solvers for this class of large scale systems of weakly nonlinear equations. (C) 2009 Published by Elsevier B.V. oil behalf of IMACS. |
| Keyword | System of weakly nonlinear equations HSS iteration method Inner/outer iteration scheme Nonlinear iteration scheme Local convergence |
| DOI | 10.1016/j.apnum.2009.06.005 |
| Language | 英语 |
| Funding Project | National Basic Research Program[2005CB321702] ; National Outstanding Young Scientist Foundation[10525102] ; National Natural Science Foundation , PR China[10471146] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000270453100004 |
| Publisher | ELSEVIER SCIENCE BV |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/7399 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Bai, Zhong-Zhi |
| Affiliation | Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Bai, Zhong-Zhi,Yang, Xi. On HSS-based iteration methods for weakly nonlinear systems[J]. APPLIED NUMERICAL MATHEMATICS,2009,59(12):2923-2936. |
| APA | Bai, Zhong-Zhi,&Yang, Xi.(2009).On HSS-based iteration methods for weakly nonlinear systems.APPLIED NUMERICAL MATHEMATICS,59(12),2923-2936. |
| MLA | Bai, Zhong-Zhi,et al."On HSS-based iteration methods for weakly nonlinear systems".APPLIED NUMERICAL MATHEMATICS 59.12(2009):2923-2936. |
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