An algorithm to describe the solution set of any tropical linear system A x=B x
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, in...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2001 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/57074 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/57074 |
| Access Level: | acceso abierto |
| Palabra clave: | 512 Tropical linear system Algorithm Álgebra 1201 Álgebra |
| Sumario: | 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. |
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