Solving nonlinear matrix equations arising in Tree-Like stochastic processes

摘要

In this paper, based on matrix structure analysis, we derive and analyze efficient algorithms to solve nonlinear matrix equations of the form X + Sigma(1less than or equal toiless than or equal tod) A(i)X(-1)D(i) = C. This class of equations is encountered in the solution of Tree-Like stochastic processes which are a generalization of Quasi-Birth-and-Death (QBD) processes. (C) 2003 Elsevier Science Inc. All rights reserved. [References: 18]