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Weak dual residuations applied to tropical linear equations

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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https://hal.univ-angers.fr/hal-02535546
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Soumis le : mardi 7 avril 2020 - 16:21:24
Dernière modification le : lundi 14 novembre 2022 - 02:46:05

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Vinicius Mariano Gonçalves, Carlos Andrey Maia, Laurent Hardouin. Weak dual residuations applied to tropical linear equations. Linear Algebra and its Applications, 2014, 445, pp.69-84. ⟨10.1016/j.laa.2013.10.044⟩. ⟨hal-02535546⟩

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