Parallel multisplitting two-stage iterative methods for large sparse systems of weakly nonlinear equations
文献类型：期刊论文
| 作者 | Bai, ZZ
|
| 刊名 | NUMERICAL ALGORITHMS
 |
| 出版日期 | 1997 |
| 卷号 | 15期号:3-4页码:347-372 |
| 关键词 | system of weakly nonlinear equations matrix multisplitting two-stage iteration relaxation technique convergence theory convergence rate |
| ISSN号 | 1017-1398 |
| 英文摘要 | The finite difference or the finite element discretizations of many differential or integral equations often result in a class of systems of weakly nonlinear equations. In this paper, by reasonably applying both the multisplitting and the two-stage iteration techniques, and in accordance with the special properties of this system of weakly nonlinear equations, we first propose a general multisplitting two-stage iteration method through the two-stage multiple splittings of the system matrix. Then, by applying the accelerated overrelaxation (AOR) technique of the linear iterative methods, we present a multisplitting two-stage AOR method, which particularly uses the AOR-like iteration as inner iteration and is substantially a relaxed variant of the afore-presented method. These two methods have a forceful parallel computing function and are much more suitable to the high-speed multiprocessor systems. For these two classes of methods, we establish their local convergence theories, and precisely estimate their asymptotic convergence factors under some suitable assumptions when the involved nonlinear mapping is only directionally differentiable. When the system matrix is either an H-matrix or a monotone matrix, and the nonlinear mapping is a P-bounded mapping, we thoroughly set up the global convergence theories of these new methods. Moreover, under the assumptions that the system matrix is monotone and the nonlinear mapping is isotone, we discuss the monotone convergence properties of the new multisplitting two-stage iteration methods, and investigate the influence of the multiple splittings as well as the relaxation parameters upon the convergence behaviours of these methods. Numerical computations show that our new methods are feasible and efficient for parallel solving of the system of weakly nonlinear equations. |
| 语种 | 英语 |
| WOS记录号 | WOS:000071957900005 |
| 出版者 | BALTZER SCI PUBL BV |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/13283]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 作者单位 | 1.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100080, Peoples R China 2.Univ Oxford, Comp Lab, Oxford OX1 3QD, England |
| 推荐引用方式 GB/T 7714 | Bai, ZZ. Parallel multisplitting two-stage iterative methods for large sparse systems of weakly nonlinear equations[J]. NUMERICAL ALGORITHMS,1997,15(3-4):347-372. |
| APA | Bai, ZZ.(1997).Parallel multisplitting two-stage iterative methods for large sparse systems of weakly nonlinear equations.NUMERICAL ALGORITHMS,15(3-4),347-372. |
| MLA | Bai, ZZ."Parallel multisplitting two-stage iterative methods for large sparse systems of weakly nonlinear equations".NUMERICAL ALGORITHMS 15.3-4(1997):347-372. |
入库方式： OAI收割
来源：数学与系统科学研究院
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