APPLICATIONS OF MAX ALGEBRA TO DIAGONAL SCALING OF MATRICES
APPLICATIONS OF MAX ALGEBRA TO DIAGONAL SCALING OF MATRICES
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DOI：
10.13001/1081-3810.1165
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发表时间：
2005
影响因子：
0.7
通讯作者：
P. Butkovic;H. Schneider
中科院分区：
文献类型：
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作者：
P. Butkovic;H. Schneider
证明了极大代数中的一个不等式的结果，并应用于矩阵的对角相似尺度定理。从而得到了几个尺度问题的所有解的集合。还介绍了矩阵到具有规定的行和列最大值的矩阵的“全项秩缩放”，以及额外的要求，即所有的最大值都是在来自不同行和列的条目处获得的。给出了一种算法，当存在这样的比例时，它就能找到它。
Results are proven on an inequality in maxalgebra and applied to theorems on the diagonal similarity scaling of matrices. Thus the set of all solutions to several scaling problems is obtained. Also introduced is the "full term rank" scaling of a matrixto a matrixwith prescribed row and column maxima with the additional requirement that all the maxima are attained at entries each from a different row and column. An algorithm which finds such a scaling when it exists is given.