Abstract. The matrix equation $\sum_{i=0}^n A_i X^i=0$, where the $A_i$'s are $m\times m$ matrices, is encountered in many applications, in particular in the numerical solution of Markov chains which model queueing problems. We provide here a unifying framework in terms of Mobius' mapping to relate different resolution algorithms. This allows us to compare algorithms like Logarithmic Reduction and Cyclic Reduction, which extend Graeffe's iteration to matrix polynomials, and Matrix Sign Function iterations, which extend Cardinal's algorithm. We devise new iterative techniques having quadratic convergence and present numerical experiments.

 <postscript>  file of the paper

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