Uncoupling the Perron eigenvector problem
Uncoupling the Perron eigenvector problem
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DOI：
10.1016/0024-3795(89)90452-7
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发表时间：
1989-03
影响因子：
1.1
通讯作者：
C. D. Meyer
中科院分区：
文献类型：
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作者：
C. D. Meyer
对于谱半径为ϱ的非负不可约矩阵a，研究了满足a π= ϱπ， π# &62的唯一归一化Perron向量π的确定；0， Σ j π j= 1。它解释了如何解开一个大矩阵分成两个或两个以上的小matrices-say P 11日P 22日…,P kk-such这一系列较小的矩阵具有以下属性:(1)每个P二世也非负不可约,所以每个P ii有独特的门阶向量π(我)。(2)每个P ii有相同的谱半径ϱa(3)可以确定π(i)的年代完全是彼此独立的,所以可以执行的计算π(i)的并行。(4)很容易将较小的Perron向量π (i)耦合在一起，以产生原始矩阵A的Perron向量π。
For a nonnegative irreducible matrix A with spectral radius ϱ, this paper is concerned with the determination of the unique normalized Perron vector π which satisfies A π= ϱπ, π# &62; 0, Σ j π j= 1. It is explained how to uncouple a large matrix A into two or more smaller matrices—say P 11, P 22,…, P kk—such that this sequence of smaller matrices has the following properties:(1) Each P ii is also nonnegative and irreducible, so that each P ii has a unique Perron vector π (i).(2) Each P ii has the same spectral radius ϱ as A.(3) It is possible to determine the π (i)'s completely independently of each other, so that one can execute the computation of the π (i)'s parallel.(4) It is easy to couple the smaller Perron vectors π (i) back together in order to produce the Perron vector π for the original matrix A.