Polynomial and Pseudopolynomial Procedures for Solving Interval Two-Sided (Max, Plus)-Linear Systems

Max-plus algebra is the similarity of the classical linear algebra with two binary operations, maximum and addition. The notation Ax = Bx, where A, B are given (interval) matrices, represents (interval) two-sided (max, plus)-linear system. For the solvability of Ax = Bx, there are some pseudopolynom...

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Autores principales:	Helena Myšková, Ján Plavka
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	interval solution solvability max-plus matrix Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/598910d008374fdaa7c7e8d03f0ac760
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id	oai:doaj.org-article:598910d008374fdaa7c7e8d03f0ac760
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spelling	oai:doaj.org-article:598910d008374fdaa7c7e8d03f0ac7602021-11-25T18:17:29ZPolynomial and Pseudopolynomial Procedures for Solving Interval Two-Sided (Max, Plus)-Linear Systems10.3390/math92229512227-7390https://doaj.org/article/598910d008374fdaa7c7e8d03f0ac7602021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2951https://doaj.org/toc/2227-7390Max-plus algebra is the similarity of the classical linear algebra with two binary operations, maximum and addition. The notation Ax = Bx, where A, B are given (interval) matrices, represents (interval) two-sided (max, plus)-linear system. For the solvability of Ax = Bx, there are some pseudopolynomial algorithms, but a polynomial algorithm is still waiting for an appearance. The paper deals with the analysis of solvability of two-sided (max, plus)-linear equations with inexact (interval) data. The purpose of the paper is to get efficient necessary and sufficient conditions for solvability of the interval systems using the property of the solution set of the non-interval system Ax = Bx. The main contribution of the paper is a transformation of weak versions of solvability to either subeigenvector problems or to non-interval two-sided (max, plus)-linear systems and obtaining the equivalent polynomially checked conditions for the strong versions of solvability.Helena MyškováJán PlavkaMDPI AGarticleinterval solutionsolvabilitymax-plus matrixMathematicsQA1-939ENMathematics, Vol 9, Iss 2951, p 2951 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	interval solution solvability max-plus matrix Mathematics QA1-939
spellingShingle	interval solution solvability max-plus matrix Mathematics QA1-939 Helena Myšková Ján Plavka Polynomial and Pseudopolynomial Procedures for Solving Interval Two-Sided (Max, Plus)-Linear Systems
description	Max-plus algebra is the similarity of the classical linear algebra with two binary operations, maximum and addition. The notation Ax = Bx, where A, B are given (interval) matrices, represents (interval) two-sided (max, plus)-linear system. For the solvability of Ax = Bx, there are some pseudopolynomial algorithms, but a polynomial algorithm is still waiting for an appearance. The paper deals with the analysis of solvability of two-sided (max, plus)-linear equations with inexact (interval) data. The purpose of the paper is to get efficient necessary and sufficient conditions for solvability of the interval systems using the property of the solution set of the non-interval system Ax = Bx. The main contribution of the paper is a transformation of weak versions of solvability to either subeigenvector problems or to non-interval two-sided (max, plus)-linear systems and obtaining the equivalent polynomially checked conditions for the strong versions of solvability.
format	article
author	Helena Myšková Ján Plavka
author_facet	Helena Myšková Ján Plavka
author_sort	Helena Myšková
title	Polynomial and Pseudopolynomial Procedures for Solving Interval Two-Sided (Max, Plus)-Linear Systems
title_short	Polynomial and Pseudopolynomial Procedures for Solving Interval Two-Sided (Max, Plus)-Linear Systems
title_full	Polynomial and Pseudopolynomial Procedures for Solving Interval Two-Sided (Max, Plus)-Linear Systems
title_fullStr	Polynomial and Pseudopolynomial Procedures for Solving Interval Two-Sided (Max, Plus)-Linear Systems
title_full_unstemmed	Polynomial and Pseudopolynomial Procedures for Solving Interval Two-Sided (Max, Plus)-Linear Systems
title_sort	polynomial and pseudopolynomial procedures for solving interval two-sided (max, plus)-linear systems
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/598910d008374fdaa7c7e8d03f0ac760
work_keys_str_mv	AT helenamyskova polynomialandpseudopolynomialproceduresforsolvingintervaltwosidedmaxpluslinearsystems AT janplavka polynomialandpseudopolynomialproceduresforsolvingintervaltwosidedmaxpluslinearsystems
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Polynomial and Pseudopolynomial Procedures for Solving Interval Two-Sided (Max, Plus)-Linear Systems

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