Reference
B. De Schutter, "Upper bounds for the index of cyclicity of a matrix," Tech.
report 98-32, ESAT-SISTA, K.U.Leuven, Leuven, Belgium, 16 pp., July 1999.
Revised version.
Abstract
We derive upper bounds for the index of cyclicity of a matrix as a function of
the size of the matrix. This result can be used in the characterization of the
ultimate behavior of 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 is
cyclic. For reducible matrices the behavior is more complex, but it is also
cyclic in nature. The length of the cycles corresponds to the index of
cyclicity of the given matrix.
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BibTeX
@techreport{DeS:98-32,
author = {De Schutter, Bart},
title = {Upper Bounds for the Index of Cyclicity of a Matrix},
number = {98-32},
institution = {ESAT-SISTA, K.U.Leuven},
address = {Leuven, Belgium},
month = jul,
year = {1999},
note = {Revised version}
}