极大代数意义下矩阵的特征值问题--一类离散事件动态系统运行周期的分析
The Eigen-Problem of Matrix in Max-Algebra--Analysis for Operating Period of A Class of DEDS
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摘要: 在分析一类离散事件动态系统的运行周期及稳定性时,必须求解极大代数意义下矩阵的 特征值及特征向量,这一直被认为是十分困难和繁复的工作.本文给出了求任一方阵特征值 及特征向量的十分简单易行的方法以及有关的定理.Abstract: In this paper, eigen-problem of matrix in Max-algebra is discussed for analyzing the periodicity (or stability) of a class of discrete event dynamic systems (DEDS). Cohen and Karp have provided some algorithms to solve eigenvalue of matrix in Max-algebra. But these algorithms are only suitable to irreducible matrices. For reducible matrices, dominant and permanent of matrix must be calculated previously, which is very troublesome. In the paper, a new simple algorithm for determining eigenvalues and eigenvectors of a matrix in Max-algebra is presented by means of analyzing period behavior of the matrix.
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Key words:
- Discrete event dynamic sy tems /
- Max-algebra /
- eigenvalue /
- eigenvector
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