Reference
B. De Schutter, "On the ultimate behavior of the sequence of consecutive powers
of a matrix in the max-plus algebra,"
Linear Algebra and Its
Applications, vol. 307, no. 1-3, pp. 103-117, Mar. 2000.
Abstract
We study the sequence of consecutive powers of a matrix in the max-plus
algebra, which has maximum and addition as its basic operations. If the matrix
is irreducible then it is well known that the ultimate behavior of the sequence
is cyclic. For reducible matrices the ultimate behavior is more complex, but it
is also cyclic in nature. We will give a detailed characterization of the rates
and periods of the ultimate behavior for a general matrix.
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BibTeX
@article{DeS:99-08,
author = {De Schutter, Bart},
title = {On the Ultimate Behavior of the Sequence of Consecutive Powers of
a Matrix in the Max-Plus Algebra},
journal = {Linear Algebra and Its Applications},
volume = {307},
number = {1--3},
pages = {103--117},
month = mar,
year = {2000}
}