Weak dual residuations applied to tropical linear equations

作者：Goncalves Vinicius Mariano^*; Maia Carlos Andrey; Hardouin Laurent

来源：Linear Algebra and Its Applications, 2014, 445: 69-84.

DOI：10.1016/j.laa.2013.10.044

• Tropical algebra
• Weak residuation
• Semimodule
• Equations
• Kleene closure

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 %26quot;strong property%26quot;. 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.

• 出版日期2014-3-15