Eigenvalue Methods for Sparse Tropical Polynomial Systems

Marianne Akian, Antoine Béreau, Stéphane Gaubert

Abstract: We develop an analogue of eigenvalue methods to construct solutions of systems of tropical polynomial equalities and inequalities. We show that solutions can be obtained by solving parametric mean payoff games, arising to approriate linearizations of the systems using tropical Macaulay matrices. We implemented specific algorithms adapted to the large scale parametric games that arise in this way, and present numerical experiments.