On visualization scaling, subeigenvectors and Kleene stars in max algebra
On visualization scaling, subeigenvectors and Kleene stars in max algebra
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DOI：
10.1016/j.laa.2009.03.040
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发表时间：
2008-08
影响因子：
1.1
通讯作者：
Sergeĭ Sergeev;H. Schneider;P. Butkovic
中科院分区：
文献类型：
--
作者：
Sergeĭ Sergeev;H. Schneider;P. Butkovic
本文的目的是研究最大代数、凸性和尺度问题之间的相互作用。后者在非负矩阵理论中得到了研究，与极大代数密切相关。一个问题是严格的可视化缩放，定义为，对于给定的非负矩阵a，一个对角线矩阵X，使得X- 1ax的所有元素小于或等于a的最大循环几何平均值，对于不在临界环上的元素具有严格的不等式。本文利用非负矩阵的最大代数子特征向量和Kleene星以及凸几何的一些概念来描述这种标度。
The purpose of this paper is to investigate the interplay arising between max algebra, convexity and scaling problems. The latter, which have been studied in nonnegative matrix theory, are strongly related to max algebra. One problem is that of strict visualization scaling, defined as, for a given nonnegative matrix A, a diagonal matrix X such that all elements of X-1AX are less than or equal to the maximum cycle geometric mean of A, with strict inequality for the entries which do not lie on critical cycles. In this paper such scalings are described by means of the max algebraic subeigenvectors and Kleene stars of nonnegative matrices as well as by some concepts of convex geometry.