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An algorithm to solve any tropical linear system A¿x:B¿x
dc.contributor.author | Lorenzo García, Elisa |
dc.contributor.author | de la Puente, María Jesús |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II |
dc.date.accessioned | 2013-03-05T12:51:33Z |
dc.date.created | 2011-03-01 |
dc.date.issued | 2011-03-01 |
dc.identifier.citation | Lorenzo, 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. |
dc.identifier.issn | 0024-3795 |
dc.identifier.uri | http://hdl.handle.net/2117/18070 |
dc.description.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. |
dc.format.extent | 18 p. |
dc.language.iso | eng |
dc.publisher | Elsevier |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal |
dc.subject.lcsh | Tropical linear system |
dc.subject.lcsh | Algorithm |
dc.title | An algorithm to solve any tropical linear system A¿x:B¿x |
dc.type | Article |
dc.subject.lemac | Algorismes |
dc.identifier.doi | 10.1016/j.laa.2011.02.014, |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | 15−04 |
dc.subject.ams | 15A06 |
dc.subject.ams | 15A39 |
dc.relation.publisherversion | http://www.sciencedirect.com/science/article/pii/S002437951100125X# |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 11626423 |
dc.description.version | Postprint (published version) |
dc.date.lift | 10000-01-01 |
local.citation.author | Lorenzo, E.; de la Puente, M. |
local.citation.publicationName | Linear algebra and its applications |
local.citation.volume | 4 |
local.citation.number | 435 |
local.citation.startingPage | 884 |
local.citation.endingPage | 901 |
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