General Transience Bounds in Tropical Linear Algebra via Nachtigall Decomposition

Bernadette Charron-Bost (1) , Thomas Nowak (2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 DYOGENE - Dynamics of Geometric Networks

We present general transience bounds in tropical linear algebra based on Nachtigall's matrix decomposition. Our approach is also applicable to reducible matrices. The core technical novelty are general bounds on the transient of the maximum of two eventually periodic sequences. Our proof is algebraic in nature, in contrast to the existing purely graph-theoretic approaches.

Domaines: Mathématique discrète [cs.DM]

Bernadette Charron-Bost, Thomas Nowak. General Transience Bounds in Tropical Linear Algebra via Nachtigall Decomposition. TROPICAL-12 - International Workshop Tropical and Idempotent Mathematics, Aug 2012, Moscou, Russia. pp.46-52. ⟨hal-00993902⟩