22 citations · 91 across the 20 of their papers we have counts for
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New bounds on the periodicity transient of the powers of a tropical matrix: using cyclicity and factor rank
Arthur Kennedy-Cochran-Patrick, Glenn Merlet, Thomas Nowak +1
Building on the weak CSR approach developed in a previous paper by Merlet, Nowak and Sergeev, we establish new bounds for the periodicity threshold of the powers of a tropical matr…
On the Tightness of Bounds for Transients of Weak CSR Expansions and Periodicity Transients of Critical Rows and Columns of Tropical Matrix Powers
Glenn Merlet, Thomas Nowak, Sergei Sergeev
We study the transients of matrices in max-plus algebra. Our approach is based on the weak CSR expansion. Using this expansion, the transient can be expressed by ,…
An Overview of Transience Bounds in Max-Plus Algebra
Thomas Nowak, Bernadette Charron-Bost
We survey and discuss upper bounds on the length of the transient phase of max-plus linear systems and sequences of max-plus matrix powers. In particular, we explain how to extend…
Weak CSR expansions and transience bounds in max-plus algebra
Glenn Merlet, Thomas Nowak, Sergei Sergeev
This paper aims to unify and extend existing techniques for deriving upper bounds on the transient of max-plus matrix powers. To this aim, we introduce the concept of weak CSR expa…
Generalizations of Bounds on the Index of Convergence to Weighted Digraphs
Glenn Merlet, Thomas Nowak, Hans Schneider +1
We study sequences of optimal walks of a growing length, in weighted digraphs, or equivalently, sequences of entries of max-algebraic matrix powers with growing exponents. It is kn…