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

TL;DR

This paper introduces a new Perron iteration method for solving quadratic vector equations in Markovian Binary Trees, demonstrating improved performance over existing methods especially near critical conditions.

Contribution

The paper presents a novel Perron-based fixed point iteration for quadratic vector equations, with theoretical convergence analysis and superior performance in challenging scenarios.

Findings

Outperforms existing methods for close-to-critical problems

Convergence analysis confirms theoretical robustness

Effective in solving quadratic vector equations in Markovian Binary Trees

Abstract

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.