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We propose a novel numerical method for solving a quadratic vector equationarising in Markovian Binary Trees. The numerical method consists in a fixedpoint iteration, expressed by means of the Perron vectors of a sequence ofnonnegative matrices. A theoretical convergence analysis is performed. Theproposed method outperforms the existing methods for close-to-criticalproblems.

A Perron iteration for the solution of a quadratic vector equation arising in Markovian Binary Trees