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Eigenvalue Methods for Sparse Tropical Polynomial Systems

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Mathematical Software – ICMS 2024 (ICMS 2024)

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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.

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Authors and Affiliations

  1. Inria, 91120, Palaiseau, France

    Marianne Akian, Antoine Béreau & Stéphane Gaubert

  2. CMAP, CNRS, École polytechnique, Institut polytechnique de Paris, 91120, Palaiseau, France

    Marianne Akian, Antoine Béreau & Stéphane Gaubert

Authors
  1. Marianne Akian
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  2. Antoine Béreau
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  3. Stéphane Gaubert
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Corresponding author

Correspondence to Antoine Béreau .

Editor information

Editors and Affiliations

  1. Imperial College London, London, UK

    Kevin Buzzard

  2. University of Buenos Aires, Buenos Aires, Argentina

    Alicia Dickenstein

  3. TU Braunschweig, Braunschweig, Germany

    Bettina Eick

  4. Georgia Institute of Technology, Atlanta, GA, USA

    Anton Leykin

  5. Durham University, Durham, UK

    Yue Ren

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Akian, M., Béreau, A., Gaubert, S. (2024). Eigenvalue Methods for Sparse Tropical Polynomial Systems. In: Buzzard, K., Dickenstein, A., Eick, B., Leykin, A., Ren, Y. (eds) Mathematical Software – ICMS 2024. ICMS 2024. Lecture Notes in Computer Science, vol 14749. Springer, Cham. https://doi.org/10.1007/978-3-031-64529-7_31

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  • DOI: https://doi.org/10.1007/978-3-031-64529-7_31

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