UA - Université d'Angers : EA7315 (Université d'Angers - 40 Rue de Rennes, BP 73532 - 49035 Angers CEDEX 01 - France)
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.
Vinicius Mariano Gonçalves, Carlos Andrey Maia, Laurent Hardouin. Weak dual residuations applied to tropical linear equations. Linear Algebra and its Applications, Elsevier, 2014, 445, pp.69-84. ⟨10.1016/j.laa.2013.10.044⟩. ⟨hal-02535546⟩