Solving matrix polynomial equations arising in queueing problems Original Research Article

The matrix equation ∑i=0nAiXi=0, where the Aiʹs are m×m matrices, is encountered in the numerical solution of Markov chains which model queueing problems. We provide here a unifying framework in terms of Möbiusʹ mapping to relate different resolution algorithms having a quadratic convergence. This allows us to compare algorithms like logarithmic reduction (LR) and cyclic reduction (CR), which extend Graeffeʹs iteration to matrix polynomials, and the invariant subspace (IS) approach, which extends Cardinalʹs algorithm. We devise new iterative techniques having quadratic convergence and present numerical experiments.