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

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

2010-06-03

arxiv.org/abs/1006.0577v1

SIAM J Linear Algebra Appl. 32 (2011), no. 1, pp. 248-261

Mathematics

Numerical Analysis

Scientific paper

10.1137/100796765

We propose a novel numerical method for solving a quadratic vector equation arising in Markovian Binary Trees. The numerical method consists in a fixed point iteration, expressed by means of the Perron vectors of a sequence of nonnegative matrices. A theoretical convergence analysis is performed. The proposed method outperforms the existing methods for close-to-critical problems.

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