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

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	A class of iteration methods based on the Moser formula for nonlinear equations in Markov chains
	Bai, ZZ
刊名	LINEAR ALGEBRA AND ITS APPLICATIONS
	1997-11-15
卷号	266 页码:219-241
ISSN号	0024-3795
英文摘要	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
出版者	ELSEVIER SCIENCE INC
WOS记录号	WOS:A1997YA27900013
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/29048]
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.