Matrix representation of formal polynomials over max-plus algebra

被引：1
|
作者：
Wang, Cailu [1 ]
Tao, Yuegang [2 ]
机构：
[1] Beijing Inst Technol, Sch Automat, Beijing 100081, Peoples R China
[2] Hebei Univ Technol, Sch Artificial Intelligence, Tianjin 300130, Peoples R China
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2021年 / 20卷 / 11期
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
Max-plus algebra; formal polynomial; matrix representation; canonical form; factorization; algorithm; LINEAR-SYSTEMS;
D O I：
10.1142/S0219498821502169
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper proposes the matrix representation of formal polynomials over max-plus algebra and obtains the maximum and minimum canonical forms of a polynomial function by standardizing this representation into a canonical form. A necessary and sufficient condition for two formal polynomials corresponding to the same polynomial function is derived. Such a matrix method is constructive and intuitive, and leads to a polynomial algorithm for factorization of polynomial functions. Some illustrative examples are presented to demonstrate the results.
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页数：27
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