Convergence and quotient convergence of iterative methods for solving singular linear equations with index one

被引：11
|
作者：
Lin, Lijing [2 ]
Wei, Yimin [1 ]
Zhang, Naimin [3 ]
机构：
[1] Fudan Univ, Educ Minist, Key Lab Nonlinear Sci, Shanghai, Peoples R China
[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
[3] Wenzhou Univ, Sch Math & Informat Sci, Wenzhou 325035, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2009年 / 430卷 / 5-6期
基金：
中国国家自然科学基金; 美国国家科学基金会;
关键词：
Group inverse; Singular linear equations; Index one; Markov chain; Iterative method; Quotient convergence; SYSTEMS; INVERSE;
D O I：
10.1016/j.laa.2008.06.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Singular systems with index one arise in many applications, such as Markov chain modelling. In this paper, We use the group inverse to characterize the convergence and quotient convergence properties of stationary iterative schemes for solving consistent singular linear systems when the index of the coefficient matrix equals one. We give necessary and Sufficient conditions for the convergence of stationary iterative methods for such problems, Next we show that for the stationary iterative method, the convergence and the quotient convergence are equivalent. (c) 2009 Elsevier Inc. All rights reserved.
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页码：1665 / 1674
页数：10
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