Conditions for the structural existence of an eigenvalue of a bipartite \((\min,\max,+)\)-system.
type: Item
instance of: scholarly article
title: Conditions for the structural existence of an eigenvalue of a bipartite \((\min,\max,+)\)-system.
zbMATH Open document ID: 1043.93025
DOI: 10.1016/S0304-3975(02)00229-3
author: Subiono
author: Jacob W. van der Woude
published in: Theoretical Computer Science
publication date: 2003-05-14T00:00:00Z
review text: The paper considers bipartite \((\min,\max,+)\)-systems of the form \[ x(k+1)= A\otimes y(k),\quad y(k+1)= B\otimes'x(k), \] where \(x\), \(y\) are vectors, \(A\), \(B\) are matrices of adequate sizes, and \(\otimes\), \(\otimes'\) denote the matrix multiplication in the sense of the \((\max,+)\)- and \((\min,+)\)-algebra, respectively. Under the mild assumption that every row in \(A\) and \(B\) contains at least a finite entry, the pair \((A,B)\) being irreducible represents a necessary and sufficient condition for the structural existence of a finite eigenvalue and a corresponding finite eigenvector. This result is also illustrated by an example.
reviewed by: Octavian Pastravanu
Mathematics Subject Classification ID: 93B60
Mathematics Subject Classification ID: 93C65
zbMATH DE Number: 1909920
zbMATH Keywords: \((\min,\max,+)\) systems
zbMATH Keywords: discrete-event systems
zbMATH Keywords: eigenvalues
zbMATH Keywords: irreducibility
MaRDI profile type: Publication
cites work: Q4304869
cites work: The power algorithm in max algebra
cites work: A constructive fixed point theorem for min-max functions
cites work: The duality theorem for min-max functions
cites work: Min-max functions
cites work: Some Spectral Properties of an Operator Associated with a Pair of Nonnegative Matrices
cites work: Eigenvalues of dynamic max-min systems
cites work: Q4763579
cites work: Q4782025
cites work: A characterization of the eigenvalue of a general (min, max, +)-system
full work available at URL: s0304-3975(02)00229-3
OpenAlex ID: W1979771058
description: scientific article; zbMATH DE number 1909920