Tropical Cramer Determinants Revisited
Combinatorics
2015-04-07 v1 Optimization and Control
Abstract
We prove general Cramer type theorems for linear systems over various extensions of the tropical semiring, in which tropical numbers are enriched with an information of multiplicity, sign, or argument. We obtain existence or uniqueness results, which extend or refine earlier results of Gondran and Minoux (1978), Plus (1990), Gaubert (1992), Richter-Gebert, Sturmfels and Theobald (2005) and Izhakian and Rowen (2009). Computational issues are also discussed; in particular, some of our proofs lead to Jacobi and Gauss-Seidel type algorithms to solve linear systems in suitably extended tropical semirings.
Cite
@article{arxiv.1309.6298,
title = {Tropical Cramer Determinants Revisited},
author = {Marianne Akian and Stéphane Gaubert and Alexander Guterman},
journal= {arXiv preprint arXiv:1309.6298},
year = {2015}
}
Comments
41 pages, 5 Figures