An algorithm to solve any tropical linear system A¿x:B¿x
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An algorithm to give an explicit description of all the solutions to any tropical linear system A⊙x=B⊙x is presented. The given system is converted into a finite (rather small) number p of pairs (S,T) of classical linear systems: a system S of equations and a system T of inequalities. The notion, introduced here, that makes p small, is called compatibility. The particular feature of both S and T is that each item (equation or inequality) is bivariate, i.e., it involves exactly two variables; one variable with coefficient 1 and the other one with -1. S is solved by Gaussian elimination. We explain how to solve T by a method similar to Gaussian elimination. To achieve this, we introduce the notion of sub-special matrix. The procedure applied to T is, therefore, called sub-specialization.
CitationLorenzo, E.; de la Puente, M. An algorithm to solve any tropical linear system A¿x:B¿x. "Linear algebra and its applications", 01 Març 2011, vol. 4, núm. 435, p. 884-901.