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A class of iteration methods based on the Moser formula for nonlinear equations in Markov chains
Bai, ZZ
1997-11-15
Source PublicationLINEAR ALGEBRA AND ITS APPLICATIONS
ISSN0024-3795
Volume266Pages:219-241
AbstractMany 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.
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:A1997YA27900013
PublisherELSEVIER SCIENCE INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29049
Collection计算数学与科学工程计算研究所
AffiliationCHINESE ACAD SCI,INST COMPUTAT MATH & SCI ENGN COMP,STATE KEY LAB SCI ENGN COMP,POB 2719,BEIJING 100080,PEOPLES R CHINA
Recommended Citation
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.
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