CSR expansions of matrix powers in max algebra
CSR expansions of matrix powers in max algebra
复制标题
最大代数中矩阵幂的 CSR 展开
DOI：
--
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
H. Schneider
中科院分区：
文献类型：
--
作者：
Sergeĭ Sergeev;H. Schneider
We study the behavior of max-algebraic powers of a reducible nonnegative n by n matrix A. We show that for t>3n^2, the powers A^t can be expanded in max-algebraic powers of the form CS^tR, where C and R are extracted from columns and rows of certain Kleene stars and S is diadonally similar to a Boolean matrix. We study the properties of individual terms and show that all terms, for a given t>3n^2, can be found in O(n^4 log n) operations. We show that the powers have a well-defined ultimate behavior, where certain terms are totally or partially suppressed, thus leading to ultimate CS^tR terms and the corresponding ultimate expansion. We apply this expansion to the question whether {A^ty, t>0} is ultimately linear periodic for each starting vector y, showing that this question can be also answered in O(n^4 log n) time. We give examples illustrating our main results.
可约谱理论及其在最大代数矩阵鲁棒性中的应用
影响因子：
1.5
作者：
Butkovic P
通讯作者：
Butkovic P