Eigenproblem for optimal-node matrices in max-plus algebra

被引：0
|
作者：
Wang, Hui-li [1 ]
Wang, Xue-ping [1 ]
机构：
[1] Sichuan Normal Univ, Coll Math & Software Sci, Chengdu, Sichuan, Peoples R China
来源：
LINEAR & MULTILINEAR ALGEBRA | 2014年 / 62卷 / 08期
基金：
中国国家自然科学基金;
关键词：
max-plus algebra; optimal-node matrix; eigenvalue; eigenvector; eigenspace; maximum cycle mean; ALGORITHM;
D O I：
10.1080/03081087.2013.807342
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The eigenproblem for optimal-node matrices in max-plus algebra is shown to be solved. First, the definition of optimal-node matrix is introduced. Then for a given optimal-node matrix, it is revealed that it is easy to find all its eigenvalues and eigenvectors, which correspond to the interval time of two continuous stages and the start times of every stage of all the machines in the multi-machine interactive production process, respectively.
引用
收藏
页码：1105 / 1113
页数：9
相关论文
共 50 条
  • [1] Eigenproblem for Queueing Systems in Max-Plus Algebra
    Gavalec, Martin
    Nemcova, Zuzana
    28TH INTERNATIONAL CONFERENCE ON MATHEMATICAL METHODS IN ECONOMICS 2010, PTS I AND II, 2010, : 156 - 161
  • [2] The robustness of interval matrices in max-plus algebra
    Myskova, H.
    Plavka, J.
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 445 : 85 - 102
  • [3] Eigenvectors of interval matrices over max-plus algebra
    Cechlárová, K
    DISCRETE APPLIED MATHEMATICS, 2005, 150 (1-3) : 2 - 15
  • [4] The max-plus algebra of exponent matrices of tiled orders
    Dokuchaev, Mikhailo
    Kirichenko, Vladimir
    Kudryavtseva, Ganna
    Plakhotnyk, Makar
    JOURNAL OF ALGEBRA, 2017, 490 : 1 - 20
  • [5] The weak robustness of interval matrices in max-plus algebra
    Plavka, Jan
    DISCRETE APPLIED MATHEMATICS, 2014, 173 : 92 - 101
  • [6] ON SPECIAL CASES OF THE GENERALIZED MAX-PLUS EIGENPROBLEM
    Butkovic, Peter
    Jones, Daniel
    SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2016, 37 (03) : 1002 - 1021
  • [7] The Cholesky Decomposition of Matrices over the Symmetrized Max-Plus Algebra
    Suroto
    Palupi, Diah Junia Eksi
    Suparwanto, Ari
    IAENG International Journal of Applied Mathematics, 2022, 52 (03):
  • [8] Max-plus: A network algebra
    Daniel-Cavalcante, Mabia
    Magalhaes, Mauricio F.
    Santos-Mendes, Rafael
    POSITIVE SYSTEMS, PROCEEDINGS, 2006, 341 : 375 - 382
  • [9] A walk on max-plus algebra
    Watanabe, Sennosuke
    Fukuda, Akiko
    Segawa, Etsuo
    Sato, Iwao
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2020, 598 : 29 - 48
  • [10] On eigenproblem for circulant matrices in max-algebra
    Plávka, J
    OPTIMIZATION, 2001, 50 (5-6) : 477 - 483
12345