General Transience Bounds in Tropical Linear Algebra via Nachtigall Decomposition

Bernadette Charron-Bost 1 Thomas Nowak 2
2 DYOGENE - Dynamics of Geometric Networks
CNRS - Centre National de la Recherche Scientifique : UMR8548, Inria Paris-Rocquencourt, DI-ENS - Département d'informatique de l'École normale supérieure
Abstract : 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.
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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⟩

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