A class of two-stage iterative methods for systems of weakly nonlinear equations

	A class of two-stage iterative methods for systems of weakly nonlinear equations
	Bai, ZZ
	1997
发表期刊	NUMERICAL ALGORITHMS
ISSN	1017-1398
卷号	14 期号:4 页码:295-319
摘要	The discretizations of many differential equations by the finite difference or the finite element methods can often result in a class of System of weakly nonlinear equations. In this paper, by applying the two-stage iteration technique and in accordance with the special properties of this weakly nonlinear system, we first propose a general two-stage iterative method through the two-stage splitting of the system matrix. Then, by applying the accelerated overrelaxation (AOR) technique of the linear iterative methods, we present a two-stage AOR method, which particularly uses the AOR iteration as the inner iteration and is substantially a relaxed variant of the afore-presented method. 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 B-differentiable. When the system matrix is either a monotone matrix or an H-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 two-stage iteration methods, and investigate the influence of the matrix splittings as well as the relaxation parameters on the convergence behaviours of these methods. Numerical computations show that our new methods are feasible and efficient for solving the system of weakly nonlinear equations.
关键词	system of weakly nonlinear equations 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:A1997XE68900002
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/29058
专题	计算数学与科学工程计算研究所
作者单位	CHINESE ACAD SCI,INST COMPUTAT MATH & SCI ENGN COMP,STATE KEY LAB SCI ENGN COMP,BEIJING 100080,PEOPLES R CHINA
推荐引用方式 GB/T 7714	Bai, ZZ. A class of two-stage iterative methods for systems of weakly nonlinear equations[J]. NUMERICAL ALGORITHMS,1997,14(4):295-319.
APA	Bai, ZZ.(1997).A class of two-stage iterative methods for systems of weakly nonlinear equations.NUMERICAL ALGORITHMS,14(4),295-319.
MLA	Bai, ZZ."A class of two-stage iterative methods for systems of weakly nonlinear equations".NUMERICAL ALGORITHMS 14.4(1997):295-319.