Kybernetika 55 no. 1, 12-23, 2019

A bound for the rank-one transient of inhomogeneous matrix products in special case

Arthur Kennedy-Cochran-Patrick, Sergeĭ Sergeev and Štefan BerežnýDOI: 10.14736/kyb-2019-1-0012

Abstract:

We consider inhomogeneous matrix products over max-plus algebra, where the matrices in the product satisfy certain assumptions under which the matrix products of sufficient length~are rank-one, as it was shown in [6] ({\it Shue,\,Anderson,\,Dey 1998}). We establish a bound on the transient after which any product of matrices whose length exceeds that bound becomes rank-one.

Keywords:

max-plus algebra, matrix product, rank-one, walk, Trellis digraph

Classification:

15A80, 68R99, 16Y60, 05C20, 05C22, 05C25

paper.pdf

References:

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