On the numerical solution of a nonlinear matrix equation in Markov chains

Authors
Guo, CH
Citation
Ch. Guo, On the numerical solution of a nonlinear matrix equation in Markov chains, LIN ALG APP, 288(1-3), 1999, pp. 175-186
Citations number
14
Categorie Soggetti
Mathematics
Journal title
LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN journal
00243795 → ACNP
Volume
288
Issue
1-3
Year of publication
1999
Pages
175 - 186
Database
ISI
SICI code
0024-3795(19990201)288:1-3<175:OTNSOA>2.0.ZU;2-V
Abstract
We consider iterative methods for the minimal nonnegative solution of the m atrix equation G = Sigma(i=0)(infinity)A(i)G(i), where the matrices A(i) ar e nonnegative and Sigma(i=0)(infinity)A(i) is stochastic. Convergence theor y for an inversion free algorithm is established. The convergence rate of t his algorithm is shown to be comparable with that of the fastest iteration among three fixed point iterations. (C) 1999 Elsevier Science Inc. All righ ts reserved.