A class of iteration methods based on the Moser formula for nonlinear equations in Markov chains

	A class of iteration methods based on the Moser formula for nonlinear equations in Markov chains
	Bai, ZZ
	1997-11-15
发表期刊	LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN	0024-3795
卷号	266 页码:219-241
摘要	Many stochastic models in queueing, inventory, communications, and dam theories, etc., result in the problem of numerically determining the minimal nonnegative solutions for a class of nonlinear matrix equations. Various iterative methods have been proposed to determine the matrices of interest. We propose a new, efficient successive-substitution Moser method and a Newton-Moser method which use the Moser formula (which, originally, is just the Schulz method). These new methods avoid the inverses of the matrices, and thus considerable savings on the computational workloads may be achieved. Moreover, they are much more suitable for implementing on parallel multiprocessor systems. Under certain conditions, we establish monotone convergence of these new methods, and prove local linear convergence for the substitution Moser method and superlinear convergence for the Newton-Moser method. (C) 1997 Elsevier Science Inc.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:A1997YA27900013
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29049
专题	计算数学与科学工程计算研究所
通讯作者	Bai, ZZ
作者单位	CHINESE ACAD SCI,INST COMPUTAT MATH & SCI ENGN COMP,STATE KEY LAB SCI ENGN COMP,POB 2719,BEIJING 100080,PEOPLES R CHINA
推荐引用方式 GB/T 7714	Bai, ZZ. A class of iteration methods based on the Moser formula for nonlinear equations in Markov chains[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,1997,266:219-241.
APA	Bai, ZZ.(1997).A class of iteration methods based on the Moser formula for nonlinear equations in Markov chains.LINEAR ALGEBRA AND ITS APPLICATIONS,266,219-241.
MLA	Bai, ZZ."A class of iteration methods based on the Moser formula for nonlinear equations in Markov chains".LINEAR ALGEBRA AND ITS APPLICATIONS 266(1997):219-241.