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An algorithm to describe the solution set of any tropical linear system A x=B x

Puente Muñoz, Maria Jesus de la and Lorenzo, Elisa (2001) An algorithm to describe the solution set of any tropical linear system A x=B x. Linear Algebra and its Applications, 435 (4). pp. 884-901. ISSN 00243795

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:Tropical linear system, Algorithm
Subjects:Sciences > Mathematics > Algebra
ID Code:12783
Deposited On:30 May 2011 07:29
Last Modified:06 Feb 2014 09:32

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