Eigenvalue Methods for Sparse Tropical Polynomial Systems

International audience ; We develop an analogue of eigenvalue methods to construct solutions of sys- tems of tropical polynomial equalities and inequalities. We show that solutions can be ob- tained 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.