Note on functional iteration technique for M/G/1 type Markov chains

被引：3

作者：

Rhee, Noah H. ^{[1
]}

机构：

[1] Univ Missouri, Dept Math & Stat, Kansas City, MO 64110 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2010年 / 432卷 / 04期

关键词：

Stochastic matrices; Minimal nonnegative solution; Markov chains; Iterative methods; Mean asymptotic convergence rate;

D O I：

10.1016/j.laa.2009.10.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A thorough theoretical explanation of the numerical behaviour of functional iteration methods for the computation of the minimal nonnegative solution G of the matrix equation X = Sigma(infinity)(i=0)X(i)A(i), arising in the numerical solution of M/G/1 type Markov chains, is given in Meini (1997) [2]. In this note we add some more results. In particular, we show that an upper bound of the mean asymptotic convergence rate of the best functional iteration method is given in terms of the second largest modulus eigenvalue of G. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：1042 / 1048

页数：7

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