@inproceedings{08f17f0d82804a9db976ee9840faab1e,
title = "Eigenvalue Methods for Sparse Tropical Polynomial Systems",
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.",
keywords = "Algorithmic complexity, Polynomial systems, Tropical geometry, Zero-sum games",
author = "Marianne Akian and Antoine B{\'e}reau and St{\'e}phane Gaubert",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; 8th International Conference on Mathematical Software, ICMS 2024 ; Conference date: 22-07-2024 Through 25-07-2024",
year = "2024",
month = jan,
day = "1",
doi = "10.1007/978-3-031-64529-7\_31",
language = "English",
isbn = "9783031645280",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "299--312",
editor = "Kevin Buzzard and Alicia Dickenstein and Bettina Eick and Anton Leykin and Yue Ren",
booktitle = "Mathematical Software – ICMS 2024 - 8th International Conference, Proceedings",
}