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Weak dual residuations applied to tropical linear equations

Authors
  • Gonçalves, Vinicius Mariano
  • Maia, Carlos Andrey
  • Hardouin, Laurent1, 2, 3, 4
  • 1 Programa de Pós-Graduação em Engenharia Elétrica
  • 2 Universidade Federal de Minas Gerais (UFMG)
  • 3 Laboratoire dʼIngénierie des Systèmes Automatisés
  • 4 Université dʼAngers
Type
Published Article
Journal
Linear Algebra and its Applications
Publisher
Elsevier
Publication Date
Jan 01, 2013
Accepted Date
Oct 28, 2013
Volume
445
Pages
69–84
Identifiers
DOI: 10.1016/j.laa.2013.10.044
Source
Elsevier
Keywords
License
Unknown

Abstract

An extension to an algorithm of R.A. Cuninghame-Green and K. Zimmermann for solving equations with residuated functions is presented. This extension relies on the concept of weak residuation and in the so-called “strong property”. It is shown that a contextualization of this method to tropical linear equations, which will be denoted as Primal Method (in contrast with the Dual Method, another algorithm described in literature), generates a non-decreasing sequence which converges to the smallest solution in a special semimodule. It is also shown the connections of this method with previously published works.

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