Parallel multisplitting two-stage iterative methods for large sparse systems of weakly nonlinear equations

	Parallel multisplitting two-stage iterative methods for large sparse systems of weakly nonlinear equations
	Bai, ZZ
	1997
发表期刊	NUMERICAL ALGORITHMS
ISSN	1017-1398
卷号	15 期号:3-4 页码:347-372
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.
关键词	system of weakly nonlinear equations matrix multisplitting two-stage iteration relaxation technique convergence theory convergence rate
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000071957900005
出版者	BALTZER SCI PUBL BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13284
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.