Solving nonlinear matrix equations arising in Tree-Like stochastic processes Original Research Article

In this paper, based on matrix structure analysis, we derive and analyze efficient algorithms to solve nonlinear matrix equations of the form X+∑1less-than-or-equals, slantiless-than-or-equals, slantdAiX−1Di=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.