Solving nonlinear matrix equations arising in Tree-Like stochastic processes

By Dario Bini, Guy Latouche, B. Meini. 2003

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Abstract 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.

Subfields: Computational Theory and Mathematics, Management Information Systems, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5a94349478adad7f5482c8fb3bdaf06841d4360e