Solving nonlinear matrix equations arising in Tree-Like stochastic processes

In this paper, based on matrix structure analysis, we derive and analyze efficient algorithms to solve nonlinear matrix equations of the form X +∑ 1⩽ i ⩽ d 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.